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

Proof of a theorem of Burke and Hodel on the cardinality of topological spaces


Author: Robert L. Blair
Journal: Proc. Amer. Math. Soc. 78 (1980), 449-450
MSC: Primary 54A25
MathSciNet review: 553393
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Abstract: Techniques of Pol are used to give a direct proof of Burke and Hodel's inequality $ \vert X\vert \leqslant {2^{\Delta (X) \cdot {\text{psw}}(X)}}$, where $ \Delta (X)$ is the discreteness character of the $ {T_1}$ space X and $ {\text{psw}}(X)$ is the point separating weight of X.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0553393-6
PII: S 0002-9939(1980)0553393-6
Keywords: Cardinality of a topological space, separating open cover, point separating weight, discreteness character
Article copyright: © Copyright 1980 American Mathematical Society