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Free Abelian topological groups and the Pontryagin-Van Kampen duality

Published online by Cambridge University Press:  17 April 2009

Vladimir Pestov
Vladimir Pestov
Affiliation:
Department of Mathematics, Victoria University of Wellington, Wellington, New Zealand, e-mail: [email protected]
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Abstract

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We study the class of Tychonoff topological spaces such that the free Abelian topological group A(X) is reflexive (satisfies the Pontryagin-van Kampen duality). Every such X must be totally path-disconnected and (if it is pseudocompact) must have a trivial first cohomotopy group π1(X). If X is a strongly zero-dimensional space which is either metrisable or compact, then A(X) is reflexive.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 2 , October 1995 , pp. 297 - 311
Copyright
Copyright © Australian Mathematical Society 1995

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