Let ~ C be a category whose objects are semigroups with topology and morphisms are closed semigroup relations, in particular, continuous homomorphisms. An object X of the category ~ C is called ~ C-closed if for each morphism Φ ⊂ X×Y in the category ~ C the image Φ(X) = {y ∈ Y : ∃x ∈ X (x, y) ∈ Φ} is closed in Y. In the paper we survey existing and new results on topological groups, which are ~...

1. Introduction This note will summarize some of the recent work on topological groups and discuss a few topics in transformation groups mainly in S 3 and S 4. In one aspect of this subject, namely the relation of general locally compact groups to Lie groups, information is now fairly complete. However in most other aspects the situation is far less satisfactory and in many areas known results ...

Hausdorff Abelian groups, Pontryagin duality and the principal.These notes provide a brief introduction to topological groups with a pdws pdf special. Charactres and Pontryagin-van Kampen duality to number theory, physics and. These notes provide a brief introduction to topological groups with a special. Section 7 is peacebuilding pdf dedicated to Pontryagin-van Kampen duality.We offer an eleme...

Introduction. Let G be a locally compact, connected topological group (satisfying the second countability axiom). Let G* be a compact space which contains a dense subset G' homeomorphic to the space G and is such that G* — G' is totally disconnected. Then, Freudenthal has proved [l, Satz IX, p. 277]1 that the set G*-G' consists of at most two distinct points. Actually, Freudenthal's theorem eve...

It is shown that under mild conditions the path-component of the identity in the dual group G* of an Abelian topological group G is precisely the union of the one-parameter subgroups of CT. This yields several corollaries, including a necessary condition for certain groups to be reflexive (to satisfy the Pontrjagin duality theorem), and a negative answer to a question of N. Noble. The main resu...

we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...

Introduction Our objectives are topological versions of the Nielsen-Schreier Theorem on subgroups of free groups, and the Kurosh Theorem on subgroups of free products of groups. It is known that subgroups of free topological groups need not be free topological [2, 6, and 9]. However we might expect a subgroup theorem when a continuous Schreier transversal exists, and we give such a result in th...

In this paper we find sufficient conditions on primitive inverse topological semigroup S under which: the inversion inv : (H(S)) (H(S)) is continuous; we show that every topologically periodic countable compact primitive inverse topological semigroups with closed H-classes is topologically isomorphic to an orthogonal sum P i2= Bi (Gi) of topological Brandt extensions Bi (Gi) of countably compac...