| Full text | |
| Author(s): |
Bellini, Matheus Koveroff
;
Boero, Ana Carolina
;
Rodrigues, Vinicius de Oliveira
;
Tomita, Artur Hideyuki
Total Authors: 4
|
| Document type: | Journal article |
| Source: | Topology and its Applications; v. 297, p. 23-pg., 2021-04-29. |
| Abstract | |
Assuming the existence ofc incomparable selective ultrafilters, we classify the non torsion Abelian groups of cardinality c that admit a countably compact group topology. We show that for each kappa is an element of [c, 2(c)] each of these groups has a countably compact group topology of weight kappa without non-trivial convergent sequences and another that has convergent sequences. Assuming the existence of 2(c) selective ultrafilters, there are at least 2(c) non homeomorphic such topologies in each case and we also show that every Abelian group of cardinality at most 2(c) is algebraically countably compact. We also show that it is consistent that every Abelian group of cardinality c that admits a countably compact group topology admits a countably compact group topology without nontrivial convergent sequences whose weight has countable cofinality. (C) 2021 Elsevier B.V. All rights reserved. (AU) | |
| FAPESP's process: | 19/01388-9 - Set Theory: Forcing and its Iterations |
| Grantee: | Vinicius de Oliveira Rodrigues |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate |
| FAPESP's process: | 19/02663-3 - Infinitary Combinatorics in General Topology and Topological Algebra |
| Grantee: | Matheus Koveroff Bellini |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate |
| 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 |
| FAPESP's process: | 16/26216-8 - Topology and sets |
| Grantee: | Artur Hideyuki Tomita |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 17/15709-6 - Ultrafilters and Topological Algebra |
| Grantee: | Matheus Koveroff Bellini |
| Support Opportunities: | Scholarships in Brazil - Doctorate |