A regular topological space having no closed subsets of cardinality $\aleph _ 2$
HTML articles powered by AMS MathViewer
- by Martin Goldstern, Haim I. Judah and Saharon Shelah
- Proc. Amer. Math. Soc. 111 (1991), 1151-1159
- DOI: https://doi.org/10.1090/S0002-9939-1991-1052572-9
- PDF | 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
- E. K. van Douwen, Cardinal functions on compact $F$-spaces, and weakly countably compact Boolean algebras, Fund. Math. 114, 235-256.
- John Gregory, Higher Souslin trees and the generalized continuum hypothesis, J. Symbolic Logic 41 (1976), no. 3, 663–671. MR 485361, DOI 10.2307/2272043 A. Hajnal and I. Juhász, On hereditarily $\alpha$-Lindelöf and $\alpha$-separable spaces II, Fund. Math. 81, 147-158.
- Kenneth Kunen and Jerry E. Vaughan (eds.), Handbook of set-theoretic topology, North-Holland Publishing Co., Amsterdam, 1984. MR 776619
- R. Hodel, Cardinal functions. I, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 1–61. MR 776620
- M. Hušek, Omitting cardinal functions by topological spaces, General topology and its relations to modern analysis and algebra, V (Prague, 1981) Sigma Ser. Pure Math., vol. 3, Heldermann, Berlin, 1983, pp. 387–394. MR 698427
- Saharon Shelah, Models with second order properties. III. Omitting types for $L(Q)$, Arch. Math. Logik Grundlag. 21 (1981), no. 1-2, 1–11. MR 625527, DOI 10.1007/BF02011630
Bibliographic 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