On the cardinality of a compact $T_ 1$ space
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- by Angelo Bella PDF
- Proc. Amer. Math. Soc. 99 (1987), 176-178 Request permission
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 ${2^{{\aleph _0}}}$.References
- Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna, Tom 47. [Mathematics Library. Vol. 47]. MR 0500779
- I. Juhász, Cardinal functions in topology, Mathematical Centre Tracts, No. 34, Mathematisch Centrum, Amsterdam, 1971. In collaboration with A. Verbeek and N. S. Kroonenberg. MR 0340021
- V. I. Malyhin, On the power of first countable $T_{1}$-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
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 99 (1987), 176-178
- MSC: Primary 54A25
- DOI: https://doi.org/10.1090/S0002-9939-1987-0866448-X
- MathSciNet review: 866448