Quotient groups of linear topological spaces

Janusz Grabowski; Wojciech Wojtyński

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The concept of topological group is a simple combination of the concepts of abstract group and topological space. The purpose of this paper is to combine the concepts of topological space and rough groups; called topological rough groups on an approximation space.

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W. F. Lamartin

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CONTENTSIntroduction................... 51. k-spaces.................... 62. k-groups.................... 14References..................... 32

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Sidney Morris (1974)

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Identifying and distinguishing various varieties of abelian topological groups

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A variety of topological groups is a class of (not necessarily Hausdorff) topological groups closed under the operations of forming subgroups, quotient groups and arbitrary products. The variety of topological groups generated by a class of topological groups is the smallest variety containing the class. In this paper methods are presented to distinguish a number of significant varieties of abelian topological groups, including the varieties generated by (i) the class of all locally...

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The purpose of this note is two-fold: firstly, to give a new and interesting result concerning separate and joint continuity, and secondly, to give a stream-lined (and self-contained) proof of the fact that "tame" CHART groups are topological groups.

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We introduce a notion of a Schwartz group, which turns out to be coherent with the well known concept of a Schwartz topological vector space. We establish several basic properties of Schwartz groups and show that free topological Abelian groups, as well as free locally convex spaces, over hemicompact k-spaces are Schwartz groups. We also prove that every hemicompact k-space topological group, in particular the Pontryagin dual of a metrizable topological group, is a Schwartz group. ...

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Varieties of Topological Groups Generated by Groups with Invariant Compact Neighbourhoods of the Identity

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Sidney A. Morris (1976)

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Extensions of topological and semitopological groups and the product operation

Aleksander V. Arhangel&#039;skii, Miroslav Hušek (2001)

Commentationes Mathematicae Universitatis Carolinae

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The main results concern commutativity of Hewitt-Nachbin realcompactification or Dieudonné completion with products of topological groups. It is shown that for every topological group $G$ that is not Dieudonné complete one can find a Dieudonné complete group $H$ such that the Dieudonné completion of $G \times H$ is not a topological group containing $G \times H$ as a subgroup. Using Korovin’s construction of $G_{δ}$ -dense orbits, we present some examples showing that some results on topological groups are not valid...