A regular topological space having no closed subsets of cardinality $\aleph _ 2$
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- by Martin Goldstern, Haim I. Judah and Saharon Shelah PDF
- Proc. Amer. Math. Soc. 111 (1991), 1151-1159 Request permission
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 ${\aleph _2}$.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 111 (1991), 1151-1159
- MSC: Primary 54A25; Secondary 03E50, 03E75
- DOI: https://doi.org/10.1090/S0002-9939-1991-1052572-9
- MathSciNet review: 1052572