| Full text | |
| Author(s): |
Tomita, Artur Hideyuki
Total Authors: 1
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| Document type: | Journal article |
| Source: | Topology and its Applications; v. 259, p. 347-364, JUN 1 2019. |
| Web of Science Citations: | 1 |
| Abstract | |
We show that if kappa <= omega and there exists a group topology without non-trivial convergent sequences on an Abelian group H such that H-n is countably compact for each n < kappa then there exists a topological group G such that G(n) is countably compact for each n < kappa and G(kappa) is not countably compact. If in addition H is torsion, then the result above holds for kappa = omega(1). Combining with other results in the literature, we show that: a) Assuming c incomparable selective ultrafilters, for each n is an element of omega, there exists a group topology on the free Abelian group G such that G(n) is countably compact and G(n+1) is not countably compact. (It was already know for omega). b) If a kappa is an element of omega boolean OR [omega] boolean OR [omega(1)], there exists in ZFC a topological group G such that G(gamma) is countably compact for each cardinal gamma < kappa and G(kappa) is not countably compact. (C) 2019 Elsevier B.V. All rights reserved. (AU) | |
| FAPESP's process: | 16/26216-8 - Topology and sets |
| Grantee: | Artur Hideyuki Tomita |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 12/01490-9 - Construction of topologies: countably compact topological groups, hyperspaces and selections and others |
| Grantee: | Artur Hideyuki Tomita |
| Support Opportunities: | Regular Research Grants |