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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On the cardinality of a compact $ T\sb 1$ space

Author: Angelo Bella
Journal: Proc. Amer. Math. Soc. 99 (1987), 176-178
MSC: Primary 54A25
MathSciNet review: 866448
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Abstract: In this paper two theorems on the cardinality of a compact $ {T_1}$ space are stated. They generalize the following result: an uncountable first countable compact $ {T_1}$ space has cardinality greater than or equal to $ {2^{{\aleph _0}}}$.

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  • [1] Ryszard Engelking, General topology, PWN—Polish Scientific Publishers, Warsaw, 1977. Translated from the Polish by the author; Monografie Matematyczne, Tom 60. [Mathematical Monographs, Vol. 60]. MR 0500780 (58 #18316b)
  • [2] 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 (49 #4778)
  • [3] V. I. Malyhin, On the power of first countable 𝑇₁-bicompacta, Topology, Vol. II (Proc. Fourth Colloq., Budapest, 1978) Colloq. Math. Soc. János Bolyai, vol. 23, North-Holland, Amsterdam-New York, 1980, pp. 827–828. MR 588826 (82g:54009)

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PII: S 0002-9939(1987)0866448-X
Article copyright: © Copyright 1987 American Mathematical Society