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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the cardinality of a topological space
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by Arthur Charlesworth PDF
Proc. Amer. Math. Soc. 66 (1977), 138-142 Request permission

Abstract:

In recent papers, B. Šapirovskiĭ, R. Pol, and R. E. Hodel have used a transfinite construction technique of Šapirovskiĭ to provide a unified treatment of fundamental inequalities in the theory of cardinal functions. Šapirovskiĭ’s technique is used in this paper to establish an inequality whose countable version states that the continuum is an upper bound for the cardinality of any Lindelöf space having countable pseudocharacter and a point-continuum separating open cover. In addition, the unified treatment is extended to include a recent theorem of Šapirovskiĭ concerning the cardinality of ${T_3}$ spaces.
References
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 66 (1977), 138-142
  • MSC: Primary 54A25
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0451184-8
  • MathSciNet review: 0451184