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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Special points in compact spaces


Author: Murray Bell
Journal: Proc. Amer. Math. Soc. 122 (1994), 619-624
MSC: Primary 54D30; Secondary 54C50, 54F65, 54G20
MathSciNet review: 1246515
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Abstract: Given a collection $ \mathcal{C}$, of cardinality $ \kappa$, of subsets of a compact space X, we prove the existence of a point x such that whenever $ C \in \mathcal{C}$ and $ X \in \bar C$, there exists a $ {G_\lambda }$-set Z with $ \lambda < \kappa $ and $ x \in Z \subset \bar C$. We investigate the case when $ \mathcal{C}$ is the collection of all cozerosets of X and also when X is a dyadic space. We apply this result to homogeneous compact spaces. Another application is a characterization of $ {2^{{\omega _1}}}$ among dyadic spaces.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1246515-5
PII: S 0002-9939(1994)1246515-5
Keywords: Compact, cozeroset, dyadic, homogeneous, point
Article copyright: © Copyright 1994 American Mathematical Society