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Remarks on the cardinality of compact spaces and their Lindelöf subspaces

Authors: A. Hajnal and I. Juhász
Journal: Proc. Amer. Math. Soc. 59 (1976), 146-148
MSC: Primary 54A25; Secondary 54D30
MathSciNet review: 0423283
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Abstract: Several applications of the Čech-Pospišil theorem are given; one of them states (under CH) that every uncountable compact space has a Lindelöf subspace of cardinality $ {\omega _1}$.

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  • [1] I. Juhász, Cardinal functions in topology, Mathematisch Centrum, Amsterdam, 1971. In collaboration with A. Verbeek and N. S. Kroonenberg; Mathematical Centre Tracts, No. 34. MR 0340021
  • [2] R. Engelking, Outline of general topology, Translated from the Polish by K. Sieklucki, North-Holland Publishing Co., Amsterdam; PWN-Polish Scientific Publishers, Warsaw; Interscience Publishers Division John Wiley & Sons, Inc., New York, 1968. MR 0230273

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Article copyright: © Copyright 1976 American Mathematical Society

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