Countably compact group topologies on the free Abelian group of size continuum (and a Wallace semigroup) from a selective ultrafilter

Author(s)

Boero, A. C. ^[1] ; Pereira, I. C. ^[2] ; Tomita, A. H. ^[3]

Affiliation

^[1] Univ Fed Abc, CMCC, Rua Abolicao S-N, BR-09210180 Santo Andre, SP - Brazil

^[2] Univ Fed Para, Inst Ciencias Exatas & Nat, Rua Augusto Correa 01, BR-66075110 Belem, Para - Brazil

^[3] Univ Sao Paulo, Dept Matemat, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil

• Document type: Journal article
• Source: ACTA MATHEMATICA HUNGARICA; v. 159, n. 2, p. 414-428, DEC 2019.
• Web of Science Citations: 1

Abstract

We prove that the existence of a selective ultrafilter implies the existence of a countably compact Hausdorff group topology on the free Abelian group of size continuum. As a consequence, we show that the existence of a selective ultrafilter implies the existence of a Wallace semigroup (i.e., a countably compact both-sided cancellative topological semigroup which is not a topologicalgroup). (AU)

• FAPESP's process: 16/26216-8 - Topology and sets
• Grantee: Artur Hideyuki Tomita
• Support Opportunities: Regular Research Grants
• FAPESP's process: 10/19272-2 - Countably compact group topologies on abelian groups
• Grantee: Ana Carolina Boero
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• 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