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.

Funding

Received by the editors April 1, 2022, and, in revised form, June 15, 2022. 2020 Mathematics Subject Classification. Primary 54B05, 03E05, 03E75; Secondary 54A35, 54G12, 03E02, 03E35. The first author was supported by CAPES (grant agreement 88882.461730/2019-01). The second author was supported by the European Research Council (grant agreement ERC-2018-StG 802756).

FundersFunder number
European CommissionERC-2018-StG 802756
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior88882.461730/2019-01

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