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

 

A regular topological space having no closed subsets of cardinality $ \aleph\sb 2$


Authors: Martin Goldstern, Haim I. Judah and Saharon Shelah
Journal: Proc. Amer. Math. Soc. 111 (1991), 1151-1159
MSC: Primary 54A25; Secondary 03E50, 03E75
MathSciNet review: 1052572
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Abstract: Using $ {\diamondsuit _{{\lambda ^ + }}}$, we construct a regular topological space in which all closed sets are of cardinality either $ < \lambda {\text{or}} \geq {{\text{2}}^{{\lambda ^ + }}}$. In particular (answering a question of Juhász) there is always a regular space in which no closed set has cardinality $ {\aleph _2}$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1052572-9
PII: S 0002-9939(1991)1052572-9
Article copyright: © Copyright 1991 American Mathematical Society