Critical ideals for countable compact spaces
Abstract
For each countable ordinal α, we introduce an ideal convα and use it to characterize the class of all compact countable spaces which are homeomorphic to the space ωα⋅ n+1 with the order topology. The characterization is expressed in terms of finding a convergent subsequence defined on a set not belonging to convα.
Fields of Study & Subjects
Advanced Topology and Set Theory
Advanced Banach Space Theory
Fuzzy and Soft Set Theory
Publication details
- Journal / source
- Fundamenta Mathematicae
- Publisher
- Institute of Mathematics, Polish Academy of Sciences
- Publication date
- 8 June 2026