On Schwartz groups

L. Außenhofer; M. J. Chasco; X. Domínguez; V. Tarieladze

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Quotient groups of linear topological spaces

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The variety of topological groups generated by the free topological group on [0,1]

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On the foundations of k-group theory

W. F. Lamartin

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

Free Compact Abelian Groups

Sidney A. Morris (1972)

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Topological Rough Groups

Nurettin Bağırmaz, İlhan İçen, Abdullah F. Özcan (2016)

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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.

Fragmentable mappings and CHART groups

Warren B. Moors (2016)

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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.

Contributions to the duality theory of abelian topological groups and to the theory of nuclear groups

Außenhofer Lydia

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Abstract For a topological group G, the group G* of continuous homomorphisms (characters) into :=z∈ℂ: |z| = 1 endowed with the compact-open topology is called the character group of G and G is named ( Pontryagin) reflexive if the canonical homomorphism $α_{G} : G \to G * *$ , x ↦ (χ ↦ χ(x)), is a topological isomorphism. A comprehensive exposition of duality theory is given here. In particular, settings closely related to the theory of vector spaces (like local quasi-convexity and the corresponding hull)...

Free products of topological groups with equal uniformities, I

Edward T. Ordman (1974)

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Free products of topological groups with equal uniformities, II

Edward T. Ordman (1974)

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Maximally almost periodic groups and varieties of topological groups

Sidney Morris (1974)

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Identifying and distinguishing various varieties of abelian topological groups

Carolyn E. McPhail, Sidney A. Morris

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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...

Remarks on Varieties of Topological Groups

Sidney A. Morris (1974)

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A relatively free topological group that is not varietal free

Vladimir Pestov, Dmitri Shakhmatov (1998)

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Answering a 1982 question of Sidney A. Morris, we construct a topological group G and a subspace X such that (i) G is algebraically free over X, (ii) G is relatively free over X, that is, every continuous mapping from X to G extends to a unique continuous endomorphism of G, and (iii) G is not a varietal free topological group on X in any variety of topological groups.