Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the cellularity of $ \beta X-X$

Authors: John Ginsburg and R. Grant Woods
Journal: Proc. Amer. Math. Soc. 57 (1976), 151-154
MSC: Primary 54A25; Secondary 54D40
MathSciNet review: 0407789
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For a topological space $ X$, let $ c(X)$ denote the cellularity of $ X$, and let $ k(X)$ denote the least cardinal of a cobase for the compact subsets of $ X$. It is shown that, if $ X$ is a completely regular Hausdorff space, $ c(\beta X - X) \leqslant {2^{c(X)k(X)}}$, and examples are given to show that this inequality is sharp. It is also shown that if $ X$ is an extremally disconnected completely regular Hausdorff space for which $ c(\beta X - X) > {2^{k(X)}}$, then $ \beta X - X$ contains a discrete $ {C^ \ast }$-embedded subspace of cardinality $ k{(X)^ + }$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54A25, 54D40

Retrieve articles in all journals with MSC: 54A25, 54D40

Additional Information

Keywords: Stone-Čech compactification, cellularity, cobase for the compact sets, extremally disconnected space
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society