Critical ideals for compact spaces

2025/03/16 by Rafał Filipów, Filipów, Rafał, Małgorzata Kowalczuk +3 · 1 voice · 1 citation
Mathematics · #03E05 (Primary) 03E10 #03E15 #03E17 #03E75 #40A05 #54A20 #54H05 (Secondary) #FOS: Mathematics #General Topology (math.GN) #math.GN

paper · pdf · doi:10.48550/arxiv.2503.12571

Abstract

For each countable ordinal α, we introduce an ideal conv_α and use it to characterize the class of all compact countable spaces which are homeomorphic to the space ω^α⋅ n+1 with the order topology. The characterization is expressed in terms of finding a convergent subsequence defined on a set not belonging to conv_α.

Cited by

• Dense-set dependence in the Katětov order for uncountable coordinate ideals

Discussions

• Rafa{\l} Filip\'ow, Ma{\l}gorzata Kowalczuk, Adam Kwela: Critical ideals for compact spaces https://arxiv.org/abs/2503.12571 https://arxiv.org/pdf/2503.12571 https://arxiv.org/html/2503.12571 [bsky, 0 points, 1 comments]

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