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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, Math. Centre Tracts, no. 34, Mathematisch Centrum, Amsterdam, 1971. MR 49 #4778. MR 0340021 (49:4778)
  • [2] R. Engelking, Outline of general topology, Biblioteka Mat., Tom 25, PWN, Warsaw, 1965; English transl., North-Holland, Amsterdam; PWN, Warsaw; Interscience, New York, 1968. MR 36 #4508; 37 #5836. MR 0230273 (37:5836)

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Article copyright: © Copyright 1976 American Mathematical Society

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