PARTITIONS OF TOPOLOGICAL SPACES AND A NEW CLUB-LIKE PRINCIPLE

Rodrigo Carvalho, Gabriel Fernandes, Lúcia R. Junqueira

Research output: Contribution to journalArticlepeer-review

Abstract

We give a new proof of the following theorem due to W. Weiss and P. Komjath: if X is a regular topological space, with character < b and X → (topω + 1)1ω, then, for all α < ω1, X → (topα)1ω, fixing a gap in the original one. For that we consider a new decomposition of topological spaces. We also define a new combinatorial principle F, and use it to prove that it is consistent with ¬CH that b is the optimal bound for the character of X. In [Proc. Amer. Math. Soc. 101 (1987), pp. 767–770], this was obtained using.

Original languageEnglish
Pages (from-to)1787-1800
Number of pages14
JournalProceedings of the American Mathematical Society
Volume151
Issue number4
DOIs
StatePublished - 1 Apr 2023

Bibliographical note

Publisher Copyright:
©2023 American Mathematical Society.

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