On the cardinality of a topological space
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- by Arthur Charlesworth
- Proc. Amer. Math. Soc. 66 (1977), 138-142
- DOI: https://doi.org/10.1090/S0002-9939-1977-0451184-8
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Abstract:
In recent papers, B. Ĺ apirovskiÄ, R. Pol, and R. E. Hodel have used a transfinite construction technique of Ĺ apirovskiÄ to provide a unified treatment of fundamental inequalities in the theory of cardinal functions. Ĺ apirovskiÄ’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 Ĺ apirovskiÄ concerning the cardinality of ${T_3}$ spaces.References
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Bibliographic 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