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Topological group

In mathematics, topological groups are the combination of groups and topological spaces, i.e. they are groups and topological spaces at the same time, such that the continuity condition for the group operations connects these two structures together and consequently they are not independent from each other.

Topological groups have been studied extensively in the period of 1925 to 1940. Haar and Weil (respectively in 1933 and 1940) showed that the integrals and Fourier series are special cases of a very wide class of topological groups.

Topological groups, along with continuous group actions, are used to study continuous symmetries, which have many applications, for example, in physics. In functional analysis, every topological vector space is an additive topological group with the additional property that scalar multiplication is continuous; consequently, many results from the theory of topological groups can be applied to functional analysis.

Formal definition
A topological group, $G$, is a topological space that is also a group such that the group operation (in this case product):

and the inversion map:

are continuous. Here $⋅ : G × G → G$ is viewed as a topological space with the product topology. Such a topology is said to be compatible with the group operations and is called a group topology.

 * Checking continuity

The product map is continuous if and only if for any $(x, y) ↦ xy$ and any neighborhood $f$ of $^{−1} : G → G$ in $W$, there exist neighborhoods $G$ of $U$ and $x$ of $V$ in $y$ such that $x ↦ x^{−1}$, where $U ⊆ G$. The inversion map is continuous if and only if for any $f^{−1}(U)$ and any neighborhood $G$ of $dom f$ in $V$, there exists a neighborhood $G$ of $U$ in $x$ such that $G × G$, where $x, y ∈ G$.

To show that a topology is compatible with the group operations, it suffices to check that the map

is continuous. Explicitly, this means that for any $xy$ and any neighborhood $G$ in $W$ of $U ⋅ V ⊆ W$, there exist neighborhoods $G$ of $U$ and $x$ of $V$ in $y$ such that $U ⋅ V := {u ⋅ v : u ∈ U, v ∈ V}$.

 * Additive notation

This definition used notation for multiplicative groups; the equivalent for additive groups would be that the following two operations are continuous:

 * Hausdorffness

Although not part of this definition, many authors require that the topology on $G$ be Hausdorff. One reason for this is that any topological group can be canonically associated with a Hausdorff topological group by taking an appropriate canonical quotient; this however, often still requires working with the original non-Hausdorff topological group. Other reasons, and some equivalent conditions, are discussed below.

This article will not assume that topological groups are necessarily Hausdorff.

 * Category

In the language of category theory, topological groups can be defined concisely as group objects in the category of topological spaces, in the same way that ordinary groups are group objects in the category of sets. Note that the axioms are given in terms of the maps (binary product, unary inverse, and nullary identity), hence are categorical definitions.

Homomorphisms
A homomorphism of topological groups means a continuous group homomorphism $x ∈ G$. Topological groups, together with their homomorphisms, form a category. A group homomorphism between topological groups is continuous if and only if it is continuous at some point.

An isomorphism of topological groups is a group isomorphism that is also a homeomorphism of the underlying topological spaces. This is stronger than simply requiring a continuous group isomorphism—the inverse must also be continuous. There are examples of topological groups that are isomorphic as ordinary groups but not as topological groups. Indeed, any non-discrete topological group is also a topological group when considered with the discrete topology. The underlying groups are the same, but as topological groups there is not an isomorphism.

Examples
Every group can be trivially made into a topological group by considering it with the discrete topology; such groups are called discrete groups. In this sense, the theory of topological groups subsumes that of ordinary groups. The indiscrete topology (i.e. the trivial topology) also makes every group into a topological group.

The real numbers, $$\mathbb{R}$$ with the usual topology form a topological group under addition. Euclidean $G$-space $x^{−1}$ is also a topological group under addition, and more generally, every topological vector space forms an (abelian) topological group. Some other examples of abelian topological groups are the circle group $U^{−1} ⊆ V$, or the torus $U^{−1} := { u^{−1} : u ∈ U }$ for any natural number $n$.

The classical groups are important examples of non-abelian topological groups. For instance, the general linear group $G × G → G$ of all invertible $n$-by-$n$ matrices with real entries can be viewed as a topological group with the topology defined by viewing $(x, y) ↦ xy^{−1}$ as a subspace of Euclidean space $x, y ∈ G$. Another classical group is the orthogonal group $xy^{−1}$, the group of all linear maps from $U ⋅ (V^{−1}) ⊆ W$ to itself that preserve the length of all vectors. The orthogonal group is compact as a topological space. Much of Euclidean geometry can be viewed as studying the structure of the orthogonal group, or the closely related group $+ : G × G → G$ of isometries of $(x, y) ↦ x + y$.

The groups mentioned so far are all Lie groups, meaning that they are smooth manifolds in such a way that the group operations are smooth, not just continuous. Lie groups are the best-understood topological groups; many questions about Lie groups can be converted to purely algebraic questions about Lie algebras and then solved.

An example of a topological group that is not a Lie group is the additive group $$\mathbb{Q}$$ of rational numbers, with the topology inherited from $$\mathbb{R}$$. This is a countable space, and it does not have the discrete topology. An important example for number theory is the group $− : G → G$ of p-adic integers, for a prime number $n$, meaning the inverse limit of the finite groups $x ↦ −x$ as n goes to infinity. The group $G → H$ is well behaved in that it is compact (in fact, homeomorphic to the Cantor set), but it differs from (real) Lie groups in that it is totally disconnected. More generally, there is a theory of p-adic Lie groups, including compact groups such as $$\mathbb{R}$^{n}$ as well as locally compact groups such as $S^{1}$, where $(S^{1})^{n}$ is the locally compact field of p-adic numbers.

The group $GL(n,$\mathbb{R}$)$ is a pro-finite group; it is isomorphic to a subgroup of the product $$\prod_{n \geq 1} \mathbb{Z} / p^n $$ in such a way that its topology is induced by the product topology, where the finite groups $$\mathbb{Z} / p^n$$ are given the discrete topology. Another large class of pro-finite groups important in number theory are absolute Galois groups.

Some topological groups can be viewed as infinite dimensional Lie groups; this phrase is best understood informally, to include several different families of examples. For example, a topological vector space, such as a Banach space or Hilbert space, is an abelian topological group under addition. Some other infinite-dimensional groups that have been studied, with varying degrees of success, are loop groups, Kac–Moody groups, Diffeomorphism groups, homeomorphism groups, and gauge groups.

In every Banach algebra with multiplicative identity, the set of invertible elements forms a topological group under multiplication. For example, the group of invertible bounded operators on a Hilbert space arises this way.

Translation invariance
Every topological group's topology is, which by definition means that if for any $$a \in G,$$ left or right multiplication by this element yields a homeomorphism $$G \to G.$$ Consequently, for any $$a \in G$$ and $$S \subseteq G,$$ the subset $$S$$ is open (resp. closed) in $$G$$ if and only if this is true of its left translation $$a S := \{a s : s \in S\}$$ and right translation $$S a := \{s a : s \in S\}.$$ If $$\mathcal{N}$$ is a neighborhood basis of the identity element in a topological group $$G$$ then for all $$x \in X,$$

is a neighborhood basis of $$x$$ in $$G.$$ In particular, any group topology on a topological group is completely determined by any neighborhood basis at the identity element. If $$S$$ is any subset of $$G$$ and $$U$$ is an open subset of $$G,$$ then $$S U := \{s u : s \in S, u \in U\}$$ is an open subset of $$G.$$

Symmetric neighborhoods
The inversion operation $$g \mapsto g^{-1}$$ on a topological group $$G$$ is a homeomorphism from $$G$$ to itself.

A subset $$S \subseteq G$$ is said to be symmetric if $$S^{-1} = S,$$ where $$S^{-1} := \left\{s^{-1} : s \in S\right\}.$$ The closure of every symmetric set in a commutative topological group is symmetric. If $p$ is any subset of a commutative topological group $S$, then the following sets are also symmetric: $GL(n,$\mathbb{R}$)$, $$\mathbb{R}$^{n×n}$, and $O(n)$.

For any neighborhood $G$ in a commutative topological group $N$ of the identity element, there exists a symmetric neighborhood $G$ of the identity element such that $$\mathbb{R}$^{n}$, where note that $O(n) ⋉ $\mathbb{R}$^{n}$ is necessarily a symmetric neighborhood of the identity element. Thus every topological group has a neighborhood basis at the identity element consisting of symmetric sets.

If $M$ is a locally compact commutative group, then for any neighborhood $G$ in $N$ of the identity element, there exists a symmetric relatively compact neighborhood $G$ of the identity element such that $$\mathbb{R}$^{n}$ (where $$\mathbb{Z}$_{p}$ is symmetric as well).

Uniform space
Every topological group can be viewed as a uniform space in two ways; the left uniformity turns all left multiplications into uniformly continuous maps while the right uniformity turns all right multiplications into uniformly continuous maps. If $M$ is not abelian, then these two need not coincide. The uniform structures allow one to talk about notions such as completeness, uniform continuity and uniform convergence on topological groups.

Separation properties
If $G$ is an open subset of a commutative topological group $U$ and $G$ contains a compact set $U$, then there exists a neighborhood $K$ of the identity element such that $$\mathbb{Z}$/p^{n}$.

As a uniform space, every commutative topological group is completely regular. Consequently, for a multiplicative topological group $N$ with identity element 1, the following are equivalent:  $G$ is a T0-space (Kolmogorov); $G$ is a T2-space (Hausdorff); $G$ is a T3$G$ (Tychonoff); $$\mathbb{Z}$_{p}$ is closed in $1/2$; $GL(n,$\mathbb{Z}$_{p})$, where $GL(n,$\mathbb{Q}$_{p})$ is a neighborhood basis of the identity element in $G$; for any $$x \in G$$ such that $$x \neq 1,$$ there exists a neighborhood $G$ in $U$ of the identity element such that $$x \not\in U.$$

A subgroup of a commutative topological group is discrete if and only if it has an isolated point.

If $G$ is not Hausdorff, then one can obtain a Hausdorff group by passing to the quotient group $$\mathbb{Q}$_{p}$, where $G$ is the closure of the identity. This is equivalent to taking the Kolmogorov quotient of $K$.

Metrisability
Let $G$ be a topological group. As with any topological space, we say that $G$ is metrisable if and only if there exists a metric $G$ on $d$, which induces the same topology on $$G$$. A metric $G$ on $d$ is called

The Birkhoff–Kakutani theorem (named after mathematicians Garrett Birkhoff and Shizuo Kakutani) states that the following three conditions on a topological group $G$ are equivalent:
 * left-invariant (resp. right-invariant) if and only if $$d(ax_{1},ax_{2})=d(x_{1},x_{2})$$(resp. $$d(x_{1}a,x_{2}a)=d(x_{1},x_{2})$$) for all $$a,x_{1},x_{2}\in G$$ (equivalently, $$d$$ is left-invariant just in case the map $$x \mapsto ax$$ is an isometry from $$(G,d)$$ to itself for each $$a \in G$$).
 * proper if and only if all open balls, $$B(r)=\{g \in G \mid d(g,1)0$$, are pre-compact.

 * 1) $G$ is (Hausdorff and) first countable (equivalently: the identity element 1 is closed in $G$, and there is a countable basis of neighborhoods for 1 in $G$).
 * 2) $G$ is metrisable (as a topological space).
 * 3) There is a left-invariant metric on $G$ that induces the given topology on $G$.
 * 4) There is a right-invariant metric on $G$ that induces the given topology on $G$.

Furthermore, the following are equivalent for any topological group $G$:

 * 1) $G$ is a second countable locally compact (Hausdorff) space.
 * 2) $G$ is a Polish, locally compact (Hausdorff) space.
 * 3) $G$ is properly metrisable (as a topological space).
 * 4) There is a left-invariant, proper metric on $G$ that induces the given topology on $G$.

Note: As with the rest of the article we of assume here a Hausdorff topology. The implications 4 $$\Rightarrow$$ 3 $$\Rightarrow$$ 2 $$\Rightarrow$$ 1 hold in any topological space. In particular 3 $$\Rightarrow$$ 2 holds, since in particular any properly metrisable space is countable union of compact metrisable and thus separable (cf. properties of compact metric spaces) subsets. The non-trivial implication 1 $$\Rightarrow$$ 4 was first proved by Raimond Struble in 1974. An alternative approach was made by Uffe Haagerup and Agata Przybyszewska in 2006, the idea of the which is as follows: One relies on the construction of a left-invariant metric, $$d_{0}$$, as in the case of first countable spaces. By local compactness, closed balls of sufficiently small radii are compact, and by normalising we can assume this holds for radius 1. Closing the open ball, $G$, of radius 1 under multiplication yields a clopen subgroup, $U$, of $H$, on which the metric $$d_{0}$$ is proper. Since $G$ is open and $H$ is second countable, the subgroup has at most countably many cosets. One now uses this sequence of cosets and the metric on $G$ to construct a proper metric on $H$.

Subgroups
Every subgroup of a topological group is itself a topological group when given the subspace topology. Every open subgroup $G$ is also closed in $H$, since the complement of $G$ is the open set given by the union of open sets $$\mathbb{Z}$_{p}$ for $S^{−1} ∩ S$. If $H$ is a subgroup of $H$ then the closure of $G$ is also a subgroup. Likewise, if $H$ is a normal subgroup of $H$, the closure of $G$ is normal in $H$.

Quotients and normal subgroups
If $G$ is a subgroup of $H$, the set of left cosets $S^{−1} ∪ S$ with the quotient topology is called a homogeneous space for $G$. The quotient map $$q : G \to G / H$$ is always open. For example, for a positive integer $G$, the sphere $S^{−1} S$ is a homogeneous space for the rotation group $M^{−1} M ⊆ N$ in $M^{−1} M$, with $cl M ⊆ N$. A homogeneous space $cl M$ is Hausdorff if and only if $n$ is closed in $H$. Partly for this reason, it is natural to concentrate on closed subgroups when studying topological groups.

If $G$ is a normal subgroup of $H$, then the quotient group $KN ⊆ U$ becomes a topological group when given the quotient topology. It is Hausdorff if and only if $G$ is closed in $H$. For example, the quotient group ${ 1 }$ is isomorphic to the circle group ${ 1 } := ∩ N ∈ 𝒩 N$.

In any topological group, the identity component (i.e., the connected component containing the identity element) is a closed normal subgroup. If $G$ is the identity component and a is any point of $C$, then the left coset $𝒩$ is the component of $G$ containing a. So the collection of all left cosets (or right cosets) of $G$ in $C$ is equal to the collection of all components of $G$. It follows that the quotient group $G/K$ is totally disconnected.

Closure and compactness
In any commutative topological group, the product (assuming the group is multiplicative) $gH$ of a compact set $G$ and a closed set $K$ is a closed set. Furthermore, for any subsets $C$ and $R$ of $S$, $g ∈ G \ H$.

If $G$ is a subgroup of a commutative topological group $H$ and if $G$ is a neighborhood in $N$ of the identity element such that $G$ is closed, then $H ∩ cl N$ is closed. Every discrete subgroup of a Hausdorff commutative topological group is closed.

Isomorphism theorems
The isomorphism theorems from ordinary group theory are not always true in the topological setting. This is because a bijective homomorphism need not be an isomorphism of topological groups.

For example, a native version of the first isomorphism theorem is false for topological groups: if $$f:G\to H$$ is a morphism of topological groups (that is, a continuous homomorphism), it is not necessarily true that the induced homomorphism $$\tilde {f}:G/\ker f\to \mathrm{Im}(f)$$ is an isomorphism of topological groups; it will be a bijective, continuous homomorphism, but it will not necessarily be a homeomorphism. In other words, it will not necessarily admit an inverse in the category of topological groups.

There is a version of the first isomorphism theorem for topological groups, which may be stated as follows: if $$f : G \to H$$ is a continuous homomorphism, then the induced homomorphism from $G/H$ to $S^{n}$ is an isomorphism if and only if the map $H$ is open onto its image.

The third isomorphism theorem, however, is true more or less verbatim for topological groups, as one may easily check.

Hilbert's fifth problem
There are several strong results on the relation between topological groups and Lie groups. First, every continuous homomorphism of Lie groups $$G \to H$$ is smooth. It follows that a topological group has a unique structure of a Lie group if one exists. Also, Cartan's theorem says that every closed subgroup of a Lie group is a Lie subgroup, in particular a smooth submanifold.

Hilbert's fifth problem asked whether a topological group $f$ that is a topological manifold must be a Lie group. In other words, does $G$ have the structure of a smooth manifold, making the group operations smooth? As shown by Andrew Gleason, Deane Montgomery, and Leo Zippin, the answer to this problem is yes. In fact, $G$ has a real analytic structure. Using the smooth structure, one can define the Lie algebra of $G$, an object of linear algebra that determines a connected group $G$ up to covering spaces. As a result, the solution to Hilbert's fifth problem reduces the classification of topological groups that are topological manifolds to an algebraic problem, albeit a complicated problem in general.

The theorem also has consequences for broader classes of topological groups. First, every compact group (understood to be Hausdorff) is an inverse limit of compact Lie groups. (One important case is an inverse limit of finite groups, called a profinite group. For example, the group $SO(n+1)$ of p-adic integers and the absolute Galois group of a field are profinite groups.) Furthermore, every connected locally compact group is an inverse limit of connected Lie groups. At the other extreme, a totally disconnected locally compact group always contains a compact open subgroup, which is necessarily a profinite group. (For example, the locally compact group $$\R$^{n+1}$ contains the compact open subgroup $S^{n} = SO(n+1)/SO(n)$, which is the inverse limit of the finite groups $G/H$ as $G$' goes to infinity.)

Representations of compact or locally compact groups
An action of a topological group $r$ on a topological space X is a group action of $G$ on X such that the corresponding function $G/H$ is continuous. Likewise, a representation of a topological group $G$ on a real or complex topological vector space V is a continuous action of $G$ on V such that for each $$\R / \Z$$, the map $S^{1}$ from V to itself is linear.

Group actions and representation theory are particularly well understood for compact groups, generalizing what happens for finite groups. For example, every finite-dimensional (real or complex) representation of a compact group is a direct sum of irreducible representations. An infinite-dimensional unitary representation of a compact group can be decomposed as a Hilbert-space direct sum of irreducible representations, which are all finite-dimensional; this is part of the Peter–Weyl theorem. For example, the theory of Fourier series describes the decomposition of the unitary representation of the circle group $aC$ on the complex Hilbert space $G/C$. The irreducible representations of $KC$ are all 1-dimensional, of the form $(cl R)(cl S) ⊆ cl (RS)$ for integers $G$ (where $G/ker(f)$ is viewed as a subgroup of the multiplicative group $n$*). Each of these representations occurs with multiplicity 1 in $im(f)$.

The irreducible representations of all compact connected Lie groups have been classified. In particular, the character of each irreducible representation is given by the Weyl character formula.

More generally, locally compact groups have a rich theory of harmonic analysis, because they admit a natural notion of measure and integral, given by the Haar measure. Every unitary representation of a locally compact group can be described as a direct integral of irreducible unitary representations. (The decomposition is essentially unique if $$$\mathbb{C}$$$ is of Type I, which includes the most important examples such as abelian groups and semisimple Lie groups.) A basic example is the Fourier transform, which decomposes the action of the additive group $$\mathbb{R}$$ on the Hilbert space $$\mathbb{Z}$_{p}$ as a direct integral of the irreducible unitary representations of $$\mathbb{R}$$. The irreducible unitary representations of $$\mathbb{R}$$ are all 1-dimensional, of the form $GL(n,$\mathbb{Q}$_{p})$ for $GL(n,$\mathbb{Z}$_{p})$.

The irreducible unitary representations of a locally compact group may be infinite-dimensional. A major goal of representation theory, related to the Langlands classification of admissible representations, is to find the unitary dual (the space of all irreducible unitary representations) for the semisimple Lie groups. The unitary dual is known in many cases such as $GL(n,$\mathbb{Z}$/p^{r})$, but not all.

For a locally compact abelian group $G$, every irreducible unitary representation has dimension 1. In this case, the unitary dual $$\hat{G}$$ is a group, in fact another locally compact abelian group. Pontryagin duality states that for a locally compact abelian group $G$, the dual of $$\hat{G}$$ is the original group $G$. For example, the dual group of the integers $G × X → X$ is the circle group $g ∈ G$, while the group $$\mathbb{R}$$ of real numbers is isomorphic to its own dual.

Every locally compact group $G$ has a good supply of irreducible unitary representations; for example, enough representations to distinguish the points of $G$ (the Gelfand–Raikov theorem). By contrast, representation theory for topological groups that are not locally compact has so far been developed only in special situations, and it may not be reasonable to expect a general theory. For example, there are many abelian Banach–Lie groups for which every representation on Hilbert space is trivial.

Homotopy theory of topological groups
Topological groups are special among all topological spaces, even in terms of their homotopy type. One basic point is that a topological group $G$ determines a path-connected topological space, the classifying space $v ↦ gv$ (which classifies principal $G$-bundles over topological spaces, under mild hypotheses). The group $G$ is isomorphic in the homotopy category to the loop space of $S^{1}$; that implies various restrictions on the homotopy type of $G$. Some of these restrictions hold in the broader context of H-spaces.

For example, the fundamental group of a topological group $G$ is abelian. (More generally, the Whitehead product on the homotopy groups of $G$ is zero.) Also, for any field k, the cohomology ring $L^{2}(S^{1})$ has the structure of a Hopf algebra. In view of structure theorems on Hopf algebras by Heinz Hopf and Armand Borel, this puts strong restrictions on the possible cohomology rings of topological groups. In particular, if $G$ is a path-connected topological group whose rational cohomology ring $S^{1}$ is finite-dimensional in each degree, then this ring must be a free graded-commutative algebra over $$\mathbb{Q}$$, that is, the tensor product of a polynomial ring on generators of even degree with an exterior algebra on generators of odd degree.

In particular, for a connected Lie group $G$, the rational cohomology ring of $G$ is an exterior algebra on generators of odd degree. Moreover, a connected Lie group $G$ has a maximal compact subgroup K, which is unique up to conjugation, and the inclusion of K into $G$ is a homotopy equivalence. So describing the homotopy types of Lie groups reduces to the case of compact Lie groups. For example, the maximal compact subgroup of $z ↦ z^{n}$ is the circle group $S^{1}$, and the homogeneous space $L^{2}(S^{1})$ can be identified with the hyperbolic plane. Since the hyperbolic plane is contractible, the inclusion of the circle group into $L^{2}($\mathbb{R}$)$ is a homotopy equivalence.

Finally, compact connected Lie groups have been classified by Wilhelm Killing, Élie Cartan, and Hermann Weyl. As a result, there is an essentially complete description of the possible homotopy types of Lie groups. For example, a compact connected Lie group of dimension at most 3 is either a torus, the group SU(2) (diffeomorphic to the 3-sphere $x ↦ e^{2πiax}$), or its quotient group $a ∈ $\mathbb{R}$$ (diffeomorphic to $SL(2,$\mathbb{R}$)$).

Complete topological group
Information about convergence of nets and filters, such as definitions and properties, can be found in the article about filters in topology.

Canonical uniformity on a commutative topological group
This article will henceforth assume that any topological group that we consider is an additive commutative topological group with identity element $$0.$$

The diagonal of $$X$$ is the set $$\Delta_X := \{(x, x) : x \in X\}$$ and for any $$N \subseteq X$$ containing $$0,$$ the canonical entourage or canonical vicinities around $$N$$ is the set $$\Delta_X(N) := \{(x, y) \in X \times X : x - y \in N\} = \bigcup_{y \in X} [(y + N) \times \{y\}] = \Delta_X + (N \times \{0\})$$

For a topological group $$(X, \tau),$$ the canonical uniformity on $$X$$ is the uniform structure induced by the set of all canonical entourages $$\Delta(N)$$ as $$N$$ ranges over all neighborhoods of $$0$$ in $$X.$$

That is, it is the upward closure of the following prefilter on $$X \times X,$$ $$\left\{\Delta(N) : N \text{ is a neighborhood of } 0 \text{ in } X\right\}$$ where this prefilter forms what is known as a base of entourages of the canonical uniformity.

For a commutative additive group $$X,$$ a fundamental system of entourages $$\mathcal{B}$$ is called a translation-invariant uniformity if for every $$B \in \mathcal{B},$$ $$(x, y) \in B$$ if and only if $$(x + z, y + z) \in B$$ for all $$x, y, z \in X.$$ A uniformity $$\mathcal{B}$$ is called translation-invariant if it has a base of entourages that is translation-invariant.

 <li>The canonical uniformity on any commutative topological group is translation-invariant.</li> <li>The same canonical uniformity would result by using a neighborhood basis of the origin rather the filter of all neighborhoods of the origin.</li> <li>Every entourage $$\Delta_X(N)$$ contains the diagonal $$\Delta_X := \Delta_X(\{0\}) = \{(x, x) : x \in X\}$$ because $$0 \in N.$$ </li> <li>If $$N$$ is symmetric (that is, $$-N = N$$) then $$\Delta_X(N)$$ is symmetric (meaning that $$\Delta_X(N)^{\operatorname{op}} = \Delta_X(N)$$) and $$\Delta_X(N) \circ \Delta_X(N) = \{(x, z) : \text{ there exists } y \in X \text{ such that } x, z \in y + N\} = \bigcup_{y \in X} [(y + N) \times (y + N)] = \Delta_X + (N \times N).$$ <li>The topology induced on $$X$$ by the canonical uniformity is the same as the topology that $$X$$ started with (that is, it is $$\tau$$).</li> </ul>

Cauchy prefilters and nets
The general theory of uniform spaces has its own definition of a "Cauchy prefilter" and "Cauchy net." For the canonical uniformity on $$X,$$ these reduces down to the definition described below.

Suppose $$x_{\bull} = \left(x_i\right)_{i \in I}$$ is a net in $$X$$ and $$y_{\bull} = \left(y_j\right)_{j \in J}$$ is a net in $$Y.$$ Make $$I \times J$$ into a directed set by declaring $$(i, j) \leq \left(i_2, j_2\right)$$ if and only if $$i \leq i_2 \text{ and } j \leq j_2.$$ Then $$x_{\bull} \times y_{\bull}: = \left(x_i, y_j\right)_{(i, j) \in I \times J}$$ denotes the product net. If $$X = Y$$ then the image of this net under the addition map $$X \times X \to X$$ denotes the sum of these two nets: $$x_{\bull} + y_{\bull}: = \left(x_i + y_j\right)_{(i, j) \in I \times J}$$ and similarly their difference is defined to be the image of the product net under the subtraction map: $$x_{\bull} - y_{\bull}: = \left(x_i - y_j\right)_{(i, j) \in I \times J}.$$

A net $$x_{\bull} = \left(x_i\right)_{i \in I}$$ in an additive topological group $$X$$ is called a Cauchy net if $$\left(x_i - x_j\right)_{(i, j) \in I \times I} \to 0 \text{ in } X$$ or equivalently, if for every neighborhood $$N$$ of $$0$$ in $$X,$$ there exists some $$i_0 \in I$$ such that $$x_i - x_j \in N$$ for all indices $$i, j \geq i_0.$$

A Cauchy sequence is a Cauchy net that is a sequence.

If $$B$$ is a subset of an additive group $$X$$ and $$N$$ is a set containing $$0,$$ then$$B$$ is said to be an $$N$$-small set or small of order $$N$$ if $$B - B \subseteq N.$$

A prefilter $$\mathcal{B}$$ on an additive topological group $$X$$ called a Cauchy prefilter if it satisfies any of the following equivalent conditions: <ol> <li>$$\mathcal{B} - \mathcal{B} \to 0$$ in $$X,$$ where $$\mathcal{B} - \mathcal{B} := \{B - C : B, C \in \mathcal{B}\}$$ is a prefilter.</li> <li>$$\{B - B : B \in \mathcal{B}\} \to 0$$ in $$X,$$ where $$\{B - B : B \in \mathcal{B}\}$$ is a prefilter equivalent to $$\mathcal{B} - \mathcal{B}.$$</li> <li>For every neighborhood $$N$$ of $$0$$ in $$X,$$ $$\mathcal{B}$$ contains some $$N$$-small set (that is, there exists some $$B \in \mathcal{B}$$ such that $$B - B \subseteq N$$).</li> </ol> and if $$X$$ is commutative then also: <li>For every neighborhood $$N$$ of $$0$$ in $$X,$$ there exists some $$B \in \mathcal{B}$$ and some $$x \in X$$ such that $$B \subseteq x + N.$$</li> </ol>
 * It suffices to check any of the above condition for any given neighborhood basis of $$0$$ in $$X.$$

Suppose $$\mathcal{B}$$ is a prefilter on a commutative topological group $$X$$ and $$x \in X.$$ Then $$\mathcal{B} \to x$$ in $$X$$ if and only if $$x \in \operatorname{cl} \mathcal{B}$$ and $$\mathcal{B}$$ is Cauchy.

Complete commutative topological group
Recall that for any $$S \subseteq X,$$ a prefilter $$\mathcal{C}$$ on $$S$$ is necessarily a subset of $$\wp(S)$$; that is, $$\mathcal{C} \subseteq \wp(S).$$

A subset $$S$$ of a topological group $$X$$ is called a complete subset if it satisfies any of the following equivalent conditions: <ol> <li>Every Cauchy prefilter $$\mathcal{C} \subseteq \wp(S)$$ on $$S$$ converges to at least one point of $$S.$$ <li>Every Cauchy net in $$S$$ converges to at least one point of $$S$$;</li> <li>Every Cauchy filter $$\mathcal{C}$$ on $$S$$ converges to at least one point of $$S.$$</li> <li>$$S$$ is a complete uniform space (under the point-set topology definition of "complete uniform space") when $$S$$ is endowed with the uniformity induced on it by the canonical uniformity of $$X$$;</li> </ol>
 * If $$X$$ is Hausdorff then every prefilter on $$S$$ will converge to at most one point of $$X.$$ But if $$X$$ is not Hausdorff then a prefilter may converge to multiple points in $$X.$$ The same is true for nets.</li>

A subset $$S$$ is called a sequentially complete subset if every Cauchy sequence in $$S$$ (or equivalently, every elementary Cauchy filter/prefilter on $$S$$) converges to at least one point of $$S.$$

 * Importantly, convergence outside of $$S$$ is allowed: If $$X$$ is not Hausdorff and if every Cauchy prefilter on $$S$$ converges to some point of $$S,$$ then $$S$$ will be complete even if some or all Cauchy prefilters on $$S$$ also converge to points(s) in the complement $$X \setminus S.$$ In short, there is no requirement that these Cauchy prefilters on $$S$$ converge only to points in $$S.$$ The same can be said of the convergence of Cauchy nets in $$S.$$
 * As a consequence, if a commutative topological group $$X$$ is not Hausdorff, then every subset of the closure of $$\{0\},$$ say $$S \subseteq \operatorname{cl} \{0\},$$ is complete (since it is clearly compact and every compact set is necessarily complete). So in particular, if $$S \neq \varnothing$$ (for example, if $$S$$ a is singleton set such as $$S = \{0\}$$) then $$S$$ would be complete even though every Cauchy net in $$S$$ (and every Cauchy prefilter on $$S$$), converges to every point in $$\operatorname{cl} \{0\}$$ (include those points in $$\operatorname{cl} \{0\}$$ that are not in $$S$$).
 * This example also shows that complete subsets (indeed, even compact subsets) of a non-Hausdorff space may fail to be closed (for example, if $$\varnothing \neq S \subseteq \operatorname{cl} \{0\}$$ then $$S$$ is closed if and only if $$S = \operatorname{cl} \{0\}$$).

A commutative topological group $$X$$ is called a complete group if any of the following equivalent conditions hold: <ol> <li>$$X$$ is complete as a subset of itself.</li> <li>Every Cauchy net in $$X$$ converges to at least one point of $$X.$$</li> <li>There exists a neighborhood of $$0$$ in $$X$$ that is also a complete subset of $$X.$$ <li>When endowed with its canonical uniformity, $$X$$ becomes is a complete uniform space. </ol>
 * This implies that every locally compact commutative topological group is complete.</li>
 * In the general theory of uniform spaces, a uniform space is called a complete uniform space if each Cauchy filter in $$X$$ converges in $$(X, \tau)$$ to some point of $$X.$$</li>

A topological group is called sequentially complete if it is a sequentially complete subset of itself.

Neighborhood basis: Suppose $$C$$ is a completion of a commutative topological group $$X$$ with $$X \subseteq C$$ and that $$\mathcal{N}$$ is a neighborhood base of the origin in $$X.$$ Then the family of sets $$\left\{ \operatorname{cl}_C N : N \in \mathcal{N} \right\}$$ is a neighborhood basis at the origin in $$C.$$

Let $$X$$ and $$Y$$ be topological groups, $$D \subseteq X,$$ and $$f : D \to Y$$ be a map. Then $$f : D \to Y$$ is uniformly continuous if for every neighborhood $$U$$ of the origin in $$X,$$ there exists a neighborhood $$V$$ of the origin in $$Y$$ such that for all $$x, y \in D,$$ if $$y - x \in U$$ then $$f(y) - f(x) \in V.$$

Generalizations
Various generalizations of topological groups can be obtained by weakening the continuity conditions:
 * A semitopological group is a group $G$ with a topology such that for each $$\mathbb{Z}$$ the two functions $S^{1}$ defined by $BG$ and $BG$ are continuous.
 * A quasitopological group is a semitopological group in which the function mapping elements to their inverses is also continuous.
 * A paratopological group is a group with a topology such that the group operation is continuous.

title: Topological group


text:
United Press International

United Press International (UPI) is an American international news agency whose newswires, photo, news film, and audio services provided news material to thousands of newspapers, magazines, radio and television stations for most of the 20th century until its eventual decline beginning in the early 1980s. At its peak, it had more than 6,000 media subscribers. Since the first of several sales and staff cutbacks in 1982, and the 1999 sale of its broadcast client list to its main U.S. rival, the Associated Press, UPI has concentrated on smaller information-market niches.

History
Formally named United Press Associations for incorporation and legal purposes but publicly known and identified as United Press or UP, the news agency was created by the 1907 uniting of three smaller news syndicates by the Midwest newspaper publisher E. W. Scripps. It was headed by Hugh Baillie (1890–1966) from 1935 to 1955. At the time of his retirement, UP had 2,900 clients in the United States, and 1,500 abroad.

In 1958, it became United Press International after absorbing the International News Service (INS) in May. As either UP or UPI, the agency was among the largest newswire services in the world, competing domestically for about 90 years with the Associated Press (AP) and internationally with AP, Reuters and Agence France-Presse (AFP).

At its peak, UPI had more than 2,000 full-time employees and 200 news bureaus in 92 countries; it had more than 6,000 media subscribers. With the rising popularity of television news, the business of UPI began to decline as the circulation of afternoon newspapers, its chief client category, began to fall. Its decline accelerated after the 1982 sale of UPI by the Scripps company.

The E.W. Scripps Company controlled United Press until its absorption of William Randolph Hearst's smaller competing agency, INS, in 1958 to form UPI. With the Hearst Corporation as a minority partner, UPI continued under Scripps management until 1982.

Since its sale in 1982, UPI has changed ownership several times and was twice in Chapter 11 bankruptcy reorganization. With each change in ownership came deeper service and staff cutbacks and changes of focus and a corresponding shrinkage of its traditional media customer base. Since the 1999 sale of its broadcast client list to its one-time major rival, the AP, UPI has concentrated on smaller information market niches. It no longer services media organizations in a major way.

In 2000, UPI was purchased by News World Communications, an international news media company founded in 1976 by Unification Church leader Sun Myung Moon.

It now maintains a news website and photo service and electronically publishes several information product packages. Based mostly on aggregation from other sources on the Web and gathered by a small editorial staff and stringers, UPI's daily content consists of a newsbrief summary service called "NewsTrack," which includes general, business, sports, science, health and entertainment reports, and "Quirks in the News." It also sells a premium service, which has deeper coverage and analysis of emerging threats, the security industry, and energy resources. UPI's content is presented in text, video and photo formats, in English, Spanish, and Arabic.

UPI's main office is in the Miami metropolitan area and it maintains office locations in five other countries and uses freelance journalists in other major cities.

United Press Associations
Beginning with the Cleveland Press, publisher E. W. Scripps (1854–1926) created the first chain of newspapers in the United States. Because the then-recently reorganized Associated Press refused to sell its services to several of his papers, most of them evening dailies in competition with existing AP franchise holders, in 1907 Scripps merged three smaller syndicates under his ownership or control, the Publishers Press Association, the Scripps-McRae Press Association, and the Scripps News Association, to form United Press Associations, with headquarters in New York City.

Scripps had been a subscriber to an earlier news agency, also named United Press, that existed in the late 1800s, partly in cooperation with the management of the original New York-based AP and partly in existential competition with two Chicago-based organizations also using the AP name (as detailed at Associated Press and in AP's 2007 history, Breaking News: How the Associated Press Has Covered War, Peace, and Everything Else, cited in Notes).

Drawing lessons from the battles between the earlier United Press and the various AP's, Scripps required that there be no restrictions on who could buy news from his news service, and he made the new UP service available to anyone, including his competitors. Scripps also hoped to make a profit from selling that news to papers owned by others. At that time and until World War II, most newspapers relied on news agencies for stories outside their immediate geographic areas.

Despite strong newspaper industry opposition, UP started to sell news to the new and competitive radio medium in 1935, years before competitor AP, controlled by the newspaper industry, did likewise.

Scripps' United Press was considered "a scrappy alternative" news source to the AP. UP reporters were called "Unipressers" and were noted for their fiercely aggressive and competitive streak. Another hallmark of the company's culture was little formal training of reporters; new hires were often thrust into a "sink-or-swim" situation of reporting on an unfamiliar subject. They were weaned on UP's famous and well-documented (though frequently misappropriated and misquoted) slogan of "Get it first, but FIRST, get it RIGHT." Despite controversy, UP (and later UPI) became a common training ground for generations of journalists.

Walter Cronkite, who started with United Press in Kansas City, gained fame for his coverage of World War II in Europe and turned down Edward R. Murrow's first offer of a CBS job to stay with UP, but who later went on to anchor the CBS Evening News, once said, "I felt every Unipresser got up in the morning saying, 'This is the day I'm going to beat the hell out of AP.' That was part of the spirit. We knew we were undermanned. But we knew we could do a darn good job despite that, and so many times, we did." Despite that, like all agencies that deal with huge volumes of timely information, UP and later UPI had its share of remembered mistakes. As recounted in the various printed histories of UPI cited in Notes, the most famous one came early in its history. UP's president, Roy W. Howard, then traveling in France, telegraphed that the 1918 armistice ending World War I had been declared four days before it happened. Howard's reputation survived and he later became a Scripps partner, whose name appeared in one of the Scripps subsidiary companies, Scripps-Howard. But the mistake dogged UP/UPI for generations. Still, the agency's reporters were often able to tell stories more quickly and accurately although they were usually outnumbered by the competition. In 1950, for example, UP reported the invasion of South Korea by North Korea two hours and forty minutes before its archrival, the AP. The New York Times later apologized to UP for refusing to print information on the invasion until the AP had confirmed it.

United Press International
Frank Bartholomew, the last UP president to ascend to the agency's top job directly from its news, rather than sales ranks, took over in 1955, and according to his memoirs cited in Notes, was obsessed with merging UP with the International News Service, a news agency that had been founded by William Randolph Hearst in 1909 following Scripps' lead.

Bartholomew succeeded in putting the "I" in UPI in 1958 when UP and INS merged to become United Press International on May 24. The new UPI now had 6,000 employees and 5,000 subscribers, about a thousand of them newspapers.

The merger was aimed at creating a stronger competitor for the Associated Press and a stronger economic entity than either UP or INS. The newly formed United Press International (UPI) had 950 client newspapers. Fearing possible antitrust issues with the Eisenhower Administration Justice Department, Scripps and Hearst rushed the merger through with unusual speed and secrecy.

Although all UP employees were retained, most INS employees lost their jobs with practically no warning. A relative few did join the new UPI and the columns of popular INS writers, such as Bob Considine, Louella Parsons and Ruth Montgomery, were carried by UPI.

Rival AP was a publishers' cooperative and could assess its members to help pay the extraordinary costs of covering major news—wars, the Olympic Games, national political conventions. UPI clients, in contrast, paid a fixed annual rate; depending on individual contracts, UPI could not always ask them to help shoulder the extraordinary coverage costs. In its heyday, newspapers typically paid UPI about half what they paid AP in the same cities for the same services: At one point, for example, the Chicago Sun-Times paid AP $12,500 a week, but UPI only $5,000; the Wall Street Journal paid AP $36,000 a week, but UPI only $19,300. The AP, which serviced 1,243 newspapers at the time, remained UPI's main competitor. In 1959, UPI had 6,208 clients in 92 countries and territories, 234 news and picture bureaus, and an annual payroll of $34,000,000, ($0 in today's dollars).

But the UP-INS merger involved another business component that was to hurt the new UPI company badly in later years. Because INS had been a subsidiary of Hearst's King Features Syndicate and Scripps controlled several other newspaper syndicates, both companies feared possible antitrust issues. So they deliberately kept their respective syndicates out of the combined UPI company. That move cost UPI the revenues of its previous United Feature Syndicate subsidiary, which in later years made large profits on the syndication of Peanuts and other popular comic strips and columns.

UPI had an advantage of independence over the AP in reporting on the Civil Rights Movement of the 1950s and 1960s. Because the AP was a cooperative essentially owned by the newspapers, those in the South influenced its coverage of the racial unrest and protests, often ignoring, minimizing, or slanting the reporting. UPI did not have that sort of pressure, and management, according to UPI reporters and photographers of the day, allowed them much freedom in chronicling the events of the civil rights struggle.

White House reporter Helen Thomas became the public face of UPI, as she was seen at televised press conferences beginning in the early 1960s. UPI famously scooped the AP in reporting the assassination of US President John Kennedy on Friday, November 22, 1963. UPI White House reporter Merriman Smith was an eyewitness, and he commandeered the press car's only phone to dictate the story to UPI as AP reporter Jack Bell tried—without success—to wrest the phone away so he could call his office. Smith and UPI won a Pulitzer Prize for this reporting.

UP/UPI Newspictures, Newsfilm and Audio/Radio Network
United Press had no direct wirephoto service until 1952, when it absorbed co-owned ACME Newspictures, under pressure from parent company Scripps to better compete with AP's news and photo services.

By that time, UP was also deeply involved with the newer visual medium of television. In 1948, it entered into a partnership with 20th Century Fox subsidiary Fox Movietone News to shoot newsfilm for television stations. That service, United Press Movietone, or UPMT, was a pioneer in newsfilm syndication and numbered among its clients major US and foreign networks and local stations, including for many years the early TV operation of ABC News. In subsequent decades, it underwent several changes in partnerships and names, becoming best known as United Press International Television News (UPITN). Senior UPITN executives later helped Ted Turner create CNN, with its first two presidents, Reese Schonfeld and Burt Reinhardt, coming from UPITN ranks.

The UPI Audio actuality service for radio stations, created in 1958 and later renamed the United Press International Radio Network, was a spinoff from the newsfilm service and eventually provided news material to more than a thousand radio stations and US and foreign networks, including NPR.

Decline
UPI came close to the size of the AP in the early 1960s, but as publishing companies began to pare their evening newspapers, it was dropped by papers that could no longer afford to subscribe to both UPI and the AP. UPI's failure to develop a television presence or subsidiary television news service has also been cited as one of the causes of its decline. By the early 1980s, the number of staffers was down to 1,800 and there were just 100 news bureaus.

Under pressure from some of E. W. Scripps' heirs, the Scripps company, which had been underwriting UPI's expenses at a loss for at least two decades, began trying to transfer control of UPI in the early 1980s. It tried to bring in additional newspaper industry partners and when that failed, engaged in serious negotiations with British competitor Reuters, which wanted to increase its US presence. As detailed in "Down to the Wire", by Gordon and Cohen, cited in Notes, Reuters did extensive due diligence and expressed an interest in parts of the UPI service, but did not wish to maintain it in full.

Scripps wound up giving the agency away to two inexperienced businessmen, Douglas Ruhe (son of David Ruhe, a member of the Universal House of Justice, the supreme governing body of the Baháʼí Faith) and William Geissler, originally associated with two better-known partners, who soon departed. Ruhe and Geissler obtained UPI for $1. Under the terms of the purchase agreement, Scripps first injected UPI with a $5 million cash balance, in acknowledgement of the $1.0 – $1.5 million per month that UPI was already losing. Facing news industry skepticism about their background and qualifications to run an international news agency, Ruhe and Geissler watched an increase in contract cancellations. Despite serious cash flow problems, they moved UPI's headquarters from New York City to Washington, DC, incurring significant additional costs due to construction cost overruns.

During this period, UPI's 25-year-old audio news actuality service for radio stations was renamed the United Press International Radio Network. But faced with recurring cash shortages and difficulty meeting payroll, the Ruhe-Geissler management sold UPI's foreign photo service and some rights to its US and foreign photos to the Reuters news agency. It also sold UPI's U.S. photo library, which included the archives of predecessor Scripps photo agency Acme and the pictures and negatives of International News Photos, the picture component of Hearst's INS to the Bettman Archive. Bettman was later sold to Microsoft founder Bill Gates's separate Corbis Corporation, storing them underground in Pennsylvania and digitizing them for licensing, frequently without any notation of their UPI origins. In August 2011 Corbis announced a deal with AP to distribute each other's photos to their clients, effectively combining the pre-1983 UPI library with that of its former main rival for some marketing purposes. In 2016 Corbis sold to the Visual China Group.

UPI's remaining minority stake in UPITN was also sold and the agency was renamed Worldwide Television News (WTN). As with its photographs, UPI thereby lost all control of its newsfilm and video library, which is now held by WTN-successor Associated Press Television News, which entered the video news field long after UPI left it.

Years of mismanagement, missed opportunities and continual wage and staff cuts followed. By 1984, UPI had descended into the first of two Chapter 11 bankruptcies. Mario Vázquez Raña, a Mexican media magnate, with a nominal American minority partner, Houston real estate developer Joseph Russo, purchased UPI out of bankruptcy for $40 million, losing millions during his short tenure, and firing numerous high-level staff.

In 1988, Vázquez Raña sold UPI to Infotechnology, Inc., an information technology and venture capital company and parent company of cable TV's Financial News Network, both headed by Earl Brian, who also became UPI chairman. In early 1991, Infotechnology itself filed for bankruptcy, announced layoffs at UPI and sought to terminate certain employee benefits in an attempt to keep UPI afloat. At that point, UPI was down to 585 employees. Later that year, UPI filed for bankruptcy for the second time, asking for relief from $50 million in debt so that it could be sale-able. In 1992, a group of Saudi investors, ARA Group International (AGI), bought the bankrupt UPI for $4 million.

By 1998, UPI had fewer than 250 employees and 12 offices. Although the Saudi-based investors claimed to have poured more than $120 million into UPI, it had failed to turn a profit. The company had begun to sell Internet-adapted products to such websites as Excite and Yahoo. At that point, UPI CEO Arnaud de Borchgrave orchestrated UPI's exit from its last major media niche, the broadcast news business that United Press had initiated in the 1930s. De Borchgrave maintained that "what was brilliant pioneering work on the part of UPI prior to World War II, with radio news, is now a static quantity and so far as I'm concerned, certainly doesn't fit into my plans for the future". He sought to shift UPI's dwindling resources into Internet-based delivery of newsletter services, focusing more on technical and diplomatic specialties than on general news. The rump UPI thus sold the client list of its still-significant radio network and broadcast wire to its former rival, the AP.

Current ownership
UPI was purchased in May 2000 by News World Communications, a media conglomerate founded by Unification Church founder Sun Myung Moon, which also owned The Washington Times and newspapers in South Korea, Japan, and South America. The next day, UPI's White House correspondent, Helen Thomas, resigned her position, after working for UPI for 57 years.

In 2007, as part of a restructuring to keep UPI in business and profitable, management cut 11 staff from its Washington, D.C. office and no longer had a reporter in the White House press corps or a bureau covering the United Nations. UPI spokespersons and press releases said the company would be focusing instead on expanding operations in the Middle East, Central Asia and Africa, and reporting on security threats, intelligence and energy issues. In 2008, UPI began UPIU, a journalism mentoring platform for students and journalism schools, that allowed recent college graduates to post their work on the site but did not pay for stories.

UPI sports awards
United Press International conferred sports awards annually until 1996. The awards were given to basketball players, basketball coaches, football players and athletes in general. The different awards were:

 * UPI Athlete of the Year

Basketball

 * UPI College Basketball Coach of the Year
 * UPI College Basketball Player of the Year

Football

 * UPI College Football Player of the Year
 * UPI College Lineman of the Year
 * UPI NFC Player of the Year
 * UPI AFL-AFC Player of the Year
 * UPI NFL Rookie of the Year
 * UPI NFL Player of the Year

Notable alumni
While much of normal news agency work is little publicized, many UP/UPI news staffers have gained fame, either while with the agency or in later careers. They include journalists, news executives, novelists and high government officials.

Among them:

 * James Atherton, veteran news photographer who caught iconic moments through a lens in Washington D.C. for over forty years
 * Rod Beaton, president and chief executive officer of United Press International from 1972 to 1982
 * David Belnap, UPI Latin American Bureau Chief and later Foreign Desk Editor for the Los Angeles Times
 * Jack Berry, UPI correspondent in Lansing, Michigan from 1956 to 1959
 * Arnaud de Borchgrave, veteran foreign correspondent and UPI executive
 * Myram Borders, longtime Las Vegas bureau manager who broke the story of Elvis Presley's marriage
 * David Brinkley, co-anchor of NBC's Huntley-Brinkley Report and anchor of ABC's This Week
 * Lucien Carr, contemporary of Allen Ginsberg and Jack Kerouac in the Beat Generation movement
 * Marquis Childs (1903–1990), later "Washington Calling" columnist
 * Raymond Clapper, originator of the term "smoke-filled room"
 * Richard Cohen, Washington Post columnist
 * Charles Collingwood, CBS News anchor, host of A Tour of the White House with Mrs. John F. Kennedy
 * Gail Collins, New York Times columnist
 * Marie Colvin, long-time war correspondent for The Sunday Times
 * Bob Considine, author of Thirty Seconds Over Tokyo and ABC and CBS radio anchor
 * Kent Cooper, who later became the longtime GM of rival Associated Press
 * Walter Cronkite, long-time anchor of the CBS Evening News
 * Bill Downs, CBS and ABC reporter, first to deliver a live broadcast from Normandy after D-Day
 * Allen Drury, Pulitzer Prize-winning novelist
 * Stephen Early, White House Press Secretary for Franklin D. Roosevelt
 * Marc S. Ellenbogen, President, The Prague Society for International Cooperation; Chair, Global Panel Foundation
 * Oscar Fraley, Untouchables co-author
 * Thomas Friedman, Three-time Pulitzer Prize-winning New York Times columnist
 * Joseph L. Galloway, military author
 * Martha Gellhorn, legendary war correspondent
 * Carmen Gentile, award-winning journalist, author and founder of Postindustrial Media
 * Henry Tilton Gorrell, filed first report on D-Day
 * Richard Helms, onetime CIA Director, who interviewed Adolf Hitler for United Press during the 1936 Olympics
 * Seymour Hersh, Pulitzer-Prize winning reporter for The New York Times, the AP and The New Yorker
 * Don Hewitt, 60 Minutes creator and producer; worked for UP Newspictures predecessor Acme Newsphotos
 * Tony Hillerman, novelist
 * Les Hinton, ex-Dow Jones CEO
 * Richard C. Hottelet, CBS News United Nations correspondent, last-surviving of the Murrow Boys
 * Brit Hume, ABC News White House Correspondent and Fox News anchor
 * David Hume Kennerly, 1970s White House photographer
 * Edward M. Korry, U.S. Ambassador to Ethiopia and Chile
 * Brian Lamb, C-SPAN founder
 * Larry LeSueur, CBS News and Voice of America White House Correspondent, two-time Peabody Award winner
 * Elmer Lower, early ABC News president
 * Eugene Lyons, former UP correspondent to Moscow, first Western journalist to interview Joseph Stalin
 * Jim McGlincy, reporter for the New York Post, New York Daily News, Newsweek and CBS News
 * Laurence Meredith, UPI international correspondent, UPI Portugal Manager, Royal Air Force veteran.
 * Knowlton Nash, Canadian journalist, senior anchor of CBC Television's flagship news program, The National
 * Ron Nessen, White House Press Secretary for Gerald Ford
 * Edwin Newman, CBS and NBC anchor, moderator of 1976 and 1984 presidential debates
 * Keith Olbermann, correspondent and host for CNN, ESPN, MSNBC, Current TV, and GQ magazine
 * Eugene Patterson, Pulitzer Prize–winning newspaper editor and columnist
 * Marjorie Paxson, influential women's page editor
 * Doc Quigg, journalist
 * George Reedy, White House Press Secretary for Lyndon Johnson
 * Harrison Salisbury, Pulitzer-Prize winner, creator of The New York Times op-ed page
 * Reese Schonfeld, co-founder of CNN
 * Robert J. Serling, novelist and brother of Rod Serling
 * Eric Sevareid, CBS News reporter, three-time Peabody Award winner
 * Neil Sheehan, reporter who broke the Pentagon Papers story for The New York Times
 * Lewis Shollenberger, CBS News reporter, ABC News, Director of Radio Liberty
 * Daniel Silva, novelist and former CNN producer
 * H. Allen Smith, best-selling author
 * Howard K. Smith, ABC Evening News anchor
 * Stan Stearns, photographer, known for picture of John F. Kennedy Jr. saluting his father's casket
 * Cyrus Leo Sulzberger II, Pulitzer-Prize winning reporter for The New York Times
 * Helen Thomas, UPI reporter from 1943 until 2000 - UPI White House Correspondent from 1961 until 2000
 * Stanley Tretick, founding photographer, People magazine
 * Hubert van Es, Saigon evacuation photographer
 * Kate Webb, war correspondent, first to reach Saigon during Tet Offensive
 * Wee Kim Wee, 4th President of Singapore
 * Weegee, Naked City photographer
 * Paul White, the founding director of CBS News
 * Steve Wilstein, who later broke the steroids scandals in baseball for the AP

UPI reporters and photographers have won ten Pulitzer Prizes:
 * Russell Jones (International Reporting, 1957)
 * Andrew Lopez (News Photography, 1960)
 * Yasushi Nagao (News Photography, 1961)
 * Merriman Smith (National Reporting, 1964)
 * Kyoichi Sawada (News Photography, 1966)
 * Toshio Sakai (Feature Photography, 1968)
 * Lucinda Franks and Thomas Powers (National Reporting, 1971)
 * David Hume Kennerly (Feature Photography, 1972)
 * John H. Blair (Spot News Photography, 1978)
 * Jahangir Razmi, (Spot News Photography, 1980)

Key UP/UPI product and technical innovation dates

 * In 1908, UP began offering feature stories and using reporter bylines.
 * In 1915, UP begins to use teleprinters, more recently known as Teletype machines.
 * In the 1930s and 1940s, UP Newspictures predecessor agency Acme developed the International Unifax machine, the first automatic picture receiver.
 * The "Ocean Press", a news service for ocean liners, was founded in the 1930s, as a corporate subsidiary of Scripps. It used copy from United Press and later United Press International. By 1959, it had 125 subscriber ships.
 * In 1935, UP was the first major news service to offer news to broadcasters.
 * In 1945, UP offered the first all-sports wire.
 * In 1948, UP started the first international television news film service. Originally named "UP Movietone", in view of a partnership with the Movietone News service of 20th Century Fox, it went through several partnerships and name changes and was known as United Press International Television News or simply as UPITN, a name which also credited UPI's film and video service partner at the time, Britain's ITN television news service.
 * In 1951, UP offered the first teletypesetter (TTS) service, enabling newspapers to automatically set and justify type from wire transmissions.
 * In 1952 UP, absorbed the Scripps-owned Acme photo service to form UP Newspictures
 * In 1958 United Press absorbed Hearst's INS to create UPI
 * In 1958, UPI created the first wire service audio network, an offshoot of the film service above. UPI Audio provided news material to radio stations. It was renamed United Press International Radio Network in 1983.
 * In 1974, UPI launched the first "high-speed" data newswire—operating at 1,200 WPM.
 * In 1978, UPI launched the first cable TV news network, UPI Newstime, using SSTV technology via satellite to relay the channel to cable TV companies nationwide in the USA.
 * In 1979, UPI along with Telecomputing Corp. of America began making the UPI world news report available to owners of home computers.
 * In 1982, UPI pioneered a coding system allowing clients to choose stories based on topic, subtopic and location.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: United Press International


text:
Pascal Lissouba

Pascal Lissouba (15 November 1931 – 24 August 2020) was a Congolese politician who was the first democratically elected President of the Republic of the Congo and served from 31 August 1992 until 25 October 1997. He was overthrown by his predecessor and current president Denis Sassou Nguesso in the 1997 civil war.

Early life and education
Lissouba was born in Tsinguidi, south-west Congo, to Bandjabi parents. He attended primary school in Mossendjo and Boko. He began his secondary studies in Brazzaville and gained his education at the Lycée Félix Faure in Nice (1948–52), where he obtained a baccalaureate. He then studied Agronomy at the École Supérieure d'Agriculture in Tunis and secured a diploma in agricultural engineering in 1956. At the University of Paris (1958–61) he received a doctoral degree in biology. He was also a fellow trainee at the National Center for Scientific Research (CNRS) in Paris and at ORSTOM. In June 1961, he worked as a researcher at ORSTOM. He was appointed lecturer in plant biology by decree of the French Ministry of National Education on 3 November 1961.

Political career
Initially he was a civil servant, working as a managing director in the Department of Agriculture (1962–63), having returned in 1962. But his abilities advanced him to become Minister of Agriculture, Livestock, Water, and Forestry on 16 August 1963 until 1966 and then Prime Minister (1963–66) under President Alphonse Massamba-Débat. He was appointed Minister of State for Planning, then for Agriculture (1968–1969), before being sacked by the government. Afterwards, he became a genetics professor at the University of Brazzaville (1966–1971) and later director of the Ecole Supérieure des Sciences in 1970. When Massamba-Débat was overthrown in 1968 Lissouba remained in government under Marien Ngouabi and although he was suspended from political activity from 1969 to 1971 he was on the Central Committee of the Congolese Workers Party in 1973.

In 1977, he was implicated for involvement in the assassination of Ngouabi and was arrested. He was sentenced to life imprisonment and hard labour in 1977. He was released in 1979 but had to live in exile in France from 1979 to 1990. In France, he was a professor of genetics at the University of Paris and then worked for UNESCO in Paris and Nairobi. When President Denis Sassou Nguesso was forced to move the Congo towards democracy in 1991, Lissouba returned in February 1992 and was elected president in the August 1992 elections. He secured 36% of the vote as head of the left-wing Pan-African Union for Social Democracy (Union panafricaine pour la démocratie sociale, UPADS). In the run-off with second-placed Bernard Kolelas, Lissouba got 61% of the vote.

Unrest and civil war
Conflict soon broke out however. A coalition of opposition groups and their militias accused Lissouba of rigging the elections. Widespread civil war was averted when Gabon and the Organisation of African Unity intervened, but sporadic fighting continued until January 1995.

Fighting broke out again in June 1997 when Lissouba engaged militias loyal to former President Col. Denis Sassou Nguesso of the Congolese Labor Party (PCT) in Brazzaville, accusing the former president of an attempted coup. Sassou Nguesso, however, was able to escape and stage a counterattack. Thus began a 4-month civil war that destroyed or damaged much of the capital. In early October 1997, Angolan troops invaded Congo on the side of Sassou. Most of Brazzaville fell to rebel and Angolan forces on 14 October 1997, and Lissouba fled; within two days the capital was under the control of forces loyal to Sassou Nguesso, and Pointe-Noire fell with little resistance. Sassou Nguesso proclaimed himself President on 25 October 1997, but militia forces loyal to Lissouba continued a guerrilla war. The vital Congo-Ocean Railway from the coastal city of Pointe-Noire was cut, and Brazzaville was heavily damaged before a cease-fire was agreed to in December 1999.

Exile and trial
Following his overthrow, Lissouba lived in exile in London. He intended to return to the Congo for the 2002 elections, but in December 2001 he was tried in absentia in Brazzaville, and sentenced to 30 years forced labor for treason and corruption, related to a $150 million oil deal with the American company Occidental Petroleum. Since 2004, he had been living in Paris in exile.

Personal life
He was first married to Annette Chantegreil, then to Jocelyne Rosdam, a French national and is the father of eleven children. His eldest daughter, Mireille Lissouba, was his chief of staff from 1993 to 1996, while his younger daughter, Danielle Bineka is a university professor and writer, both currently exiled in Canada. His mother, Marie Bouanga died in 1996.

Death
Lissouba died in Perpignan, France, on 24 August 2020, due to complications from Alzheimer's disease, aged 88.

title: Pascal Lissouba