On the cardinality of a topology
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- by Ruan Yongbin PDF
- Proc. Amer. Math. Soc. 102 (1988), 696-698 Request permission
Abstract:
Let $o\left ( X \right )$ denote the cardinality of topology of a space $X$. I. Juhasz proves that $o{\left ( X \right )^\omega } = o\left ( X \right )$ for regular hereditarily paracompact spaces. We prove it for more general classes of spaces.References
- I. Juhász, Two set-theoretic problems in topology, General topology and its relations to modern analysis and algebra, IV (Proc. Fourth Prague Topological Sympos., Prague, 1976) Lecture Notes in Math., Vol. 609, Springer, Berlin, 1977, pp. 115–123. MR 0458350 —, Cardinal functions in topology—Ten years later, MCT 123, Mathematisch Centrum, Amsterdam, 1980. E. K. Van Douwen and Zhou Hao-Xuan, The number of cozero-sets is an $\omega$-power, 1980.
- H. R. Bennett and D. J. Lutzer, A note on weak $\theta$-refinability, General Topology and Appl. 2 (1972), 49–54. MR 301697
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 102 (1988), 696-698
- MSC: Primary 54A25; Secondary 04A10
- DOI: https://doi.org/10.1090/S0002-9939-1988-0929005-3
- MathSciNet review: 929005