On powers of countably pracompact groups
Abstract
In 1990, Comfort asked: is there, for every cardinal number , a topological group such that is countably compact for all cardinals , but is not countably compact? A similar question can also be asked for countably pracompact groups: for which cardinals is there a topological group such that is countably pracompact for all cardinals , but is not countably pracompact? In this paper we construct such group in the case , assuming the existence of incomparable selective ultrafilters, and in the case , with , assuming the existence of incomparable selective ultrafilters. In particular, under the second assumption, there exists a topological group so that is countably pracompact, but is not countably pracompact, unlike the countably compact case.
Keywords
Cite
@article{arxiv.2211.14598,
title = {On powers of countably pracompact groups},
author = {Artur Hideyuki Tomita and Juliane Trianon-Fraga},
journal= {arXiv preprint arXiv:2211.14598},
year = {2022}
}