Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5775270 | Journal of Mathematical Analysis and Applications | 2017 | 14 Pages |
Abstract
Let G be a precompact, bounded torsion abelian group and Gp⧠its dual group endowed with the topology of pointwise convergence. We prove that if G is Baire (resp., pseudocompact), then all compact (resp., countably compact) subsets of Gp⧠are finite. We also prove that G is pseudocompact if and only if all countable subgroups of Gp⧠are closed. We present other characterizations of pseudocompactness and the Baire property of Gp⧠in terms of properties that express in different ways the abundance of continuous characters of G. Besides, we give an example of a precompact boolean group G with the Baire property such that the dual group Gp⧠contains an infinite countably compact subspace without isolated points.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
M.J. Chasco, X. DomÃnguez, M. Tkachenko,