Remarks on Varieties of Topological Groups

Sidney A. Morris

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Free Compact Abelian Groups

Sidney A. Morris (1972)

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

Sidney A. Morris, N. Kelly (1975)

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Maximally almost periodic groups and varieties of topological groups

Sidney Morris (1974)

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Varieties of topological groups a survey

Sidney A. Morris (1982)

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

Sidney A. Morris (1976)

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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...

Locally compact groups and β-varieties of topological groups

Sidney Morris (1973)

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On varieties of topological groups generated by solvable groups

Sidney A. Morris (1972)

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Lie groups in 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.