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Proceedings of the American Mathematical Society

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



Chains and discrete sets in zero-dimensional compact spaces

Authors: Murray Bell and John Ginsburg
Journal: Proc. Amer. Math. Soc. 83 (1981), 149-152
MSC: Primary 54A25
MathSciNet review: 620002
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Abstract: Let $ X$ be a compact zero-dimensional space and let $ B(X)$ denote the Boolean algebra of all clopen subsets of $ X$. Let $ \kappa $ be an infinite cardinal. It is shown that if $ B(X)$ contains a chain of cardinality $ \kappa $ then $ X \times X$ contains a discrete subset of cardinality $ \kappa $. This complements a recent result of J. Baumgartner and P. Komjath relating antichains in $ B(X)$ to the $ \pi $-weight of $ X$.

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

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  • [J] I. Juhász, Cardinal functions in topology, Mathematisch Centrum, Amsterdam, 1971. In collaboration with A. Verbeek and N. S. Kroonenberg; Mathematical Centre Tracts, No. 34. MR 0340021

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Keywords: Discrete set, compact zero-dimensional space, chain, antichain, strong antichain
Article copyright: © Copyright 1981 American Mathematical Society

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