Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6419232 | Journal of Mathematical Analysis and Applications | 2012 | 7 Pages |
Abstract
Given a topological group G we denote by Gâ§ the group of characters on G and reflexivity of G means that the natural map from G to Gâ§â§ is a topological isomorphism.We show that for any zero-dimensional realcompact k-space X and a discrete finitely generated abelian group A, the group AX of continuous maps from X to A with pointwise addition and compact-open topology is reflexive, and we construct a countable non-reflexive closed subgroup of ZX, where X is a countable subspace of the plane (this group embeds as a closed subgroup in many copies of the product (âZ)c of continuum of the discrete Specker group). We show also that, for metrizable separable X, analyticity of (ZX)â§ is equivalent to complete metrizability of X.
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
Roman Pol, Filip Smentek,