On countably compact group topologies without non-trivial convergent sequences on Q((kappa)) for arbitrarily large kappa and a selective ultrafilter

Author(s)

Bellini, Matheus Koveroff ^[1] ; Rodrigues, Vinicius de Oliveira ^[1] ; Tomita, Artur Hideyuki ^[1]

Affiliation

^[1] Univ Sao Paulo, Dept Matemat, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil

• Document type: Journal article
• Source: Topology and its Applications; v. 294, MAY 1 2021.
• Web of Science Citations: 0

Abstract

Castro Pereira and Tomita showed that it is consistent that there exist arbitrarily large countably compact groups without non-trivial convergent sequences of finite order. In this paper, we obtain large p-compact groups without non-trivial convergent on the direct sum of kappa copies of Q where kappa = kappa(omega) is infinite. In particular this gives the first arbitrarily large countably compact groups without non-trivial convergent sequences that are torsion-free. (C) 2021 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: 17/15502-2 - Mad Families, Forcing and Combinatorial Principles in Topology
• Grantee: Vinicius de Oliveira Rodrigues
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 17/15709-6 - Ultrafilters and Topological Algebra
• Grantee: Matheus Koveroff Bellini
• Support Opportunities: Scholarships in Brazil - Doctorate