Critical ideals for countable compact spaces
Volume 274 / 2026
Fundamenta Mathematicae 274 (2026), 1-23
MSC: Primary 54A20; Secondary 03E05, 03E10, 03E15, 03E17, 03E75, 40A05, 54H05
DOI: 10.4064/fm250316-25-1
Published online: 8 June 2026
Abstract
For each countable ordinal $\alpha $, we introduce an ideal ${\rm conv}_\alpha $ and use it to characterize the class of all compact countable spaces which are homeomorphic to the space $\omega ^{\alpha }\cdot $ $n+1$ with the order topology. The characterization is expressed in terms of finding a convergent subsequence defined on a set not belonging to ${\rm conv}_\alpha $.
