Countably compact group topologies on arbitrarily large free Abelian groups

Journal article (2023)

Authors

Matheus K. Bellini Universidade de São Paulo
K.P. Hart Analysis - EEMCS
Vinicius O. Rodrigues Universidade de São Paulo, York University
Artur H. Tomita Universidade de São Paulo
Research Group
Analysis (EEMCS) (TU Delft)
Copyright: © 2023 Matheus K. Bellini, K.P. Hart, Vinicius O. Rodrigues, Artur H. Tomita
DOI: https://doi.org/10.1016/j.topol.2023.108538
Countable compactness Free Abelian group Selective ultrafilter Topological group Wallace's problem
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Published Date

2023

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

Abstract

We prove that if there are c incomparable selective ultrafilters then, for every infinite cardinal κ such that κω=κ, there exists a group topology on the free Abelian group of cardinality κ without nontrivial convergent sequences and such that every finite power is countably compact. In particular, there are arbitrarily large countably compact groups. This answers a 1992 question of D. Dikranjan and D. Shakhmatov.