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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the cardinality of a topology

Author: Ruan Yongbin
Journal: Proc. Amer. Math. Soc. 102 (1988), 696-698
MSC: Primary 54A25; Secondary 04A10
MathSciNet review: 929005
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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 [Enhancements On Off] (What's this?)

  • [1] 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) Springer, Berlin, 1977, pp. 115–123. Lecture Notes in Math., Vol. 609. MR 0458350
  • [2] -, Cardinal functions in topology--Ten years later, MCT 123, Mathematisch Centrum, Amsterdam, 1980.
  • [3] E. K. Van Douwen and Zhou Hao-Xuan, The number of cozero-sets is an $ \omega $-power, 1980.
  • [4] H. R. Bennett and D. J. Lutzer, A note on weak 𝜃-refinability, General Topology and Appl. 2 (1972), 49–54. MR 0301697

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Keywords: Hereditary paracompactness, weak $ \theta $-refinability, weakly collectionwise normality
Article copyright: © Copyright 1988 American Mathematical Society