TY - JOUR

T1 - PARTITIONS OF TOPOLOGICAL SPACES AND A NEW CLUB-LIKE PRINCIPLE

AU - Carvalho, Rodrigo

AU - Fernandes, Gabriel

AU - Junqueira, Lúcia R.

N1 - Publisher Copyright:
©2023 American Mathematical Society.

PY - 2023/4/1

Y1 - 2023/4/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85149107235&partnerID=8YFLogxK

U2 - 10.1090/proc/16208

DO - 10.1090/proc/16208

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AN - SCOPUS:85149107235

SN - 0002-9939

VL - 151

SP - 1787

EP - 1800

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 4

ER -