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 Gpâ§ 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 Gpâ§ are finite. We also prove that G is pseudocompact if and only if all countable subgroups of Gpâ§ are closed. We present other characterizations of pseudocompactness and the Baire property of Gpâ§ 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 Gpâ§ 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,