Review

On the cardinality of S(n)-Spaces

Published in: Quaestiones Mathematicae
Volume 44 , issue 1 , 2021 , pages: 121–128

DOI: 10.2989/16073606.2019.1672112

Author(s): Alexander V. Osipov , Russia

Keywords: 54A25 , 54D10 , 54D25 , 54A25 , 54D10 , 54D25

Abstract

In this paper, for a topological space X and any positive integer n, we define the cardinal functions sL_θ _(n) (X), θ(n)-quasi-Menger number qM _θ(n) (X) and s(n)-quasi-Menger number qM _s(n) (X). We prove the following statements:

For every S(2n)-space X, |X| ≤ 2 ^sL θ (n) (X) κ_{θ (} _n ₎ (X).

For every S(2n)-space X, |X| ≤ 2 ^qM θ (n) (X) κ_{θ (} _n ₎ (X).

For every S(2n)-space X, |X| ≤ 2 ^qM s (n) (X) κ_{θ (} _n ₎ (X).

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Review

On the cardinality of S(n)-Spaces

Abstract

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