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Proceedings of the American Mathematical Society

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On the cardinality of a topological space


Author: Arthur Charlesworth
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0451184-8
Keywords: Cardinality, Lindelöf degree, pseudocharacter, separating open cover, cellularity, $ \pi $-character, cardinal function
Article copyright: © Copyright 1977 American Mathematical Society