On the cardinality of S(n)-Spaces

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).

Similar results are stated for S(2n − 1)-spaces.

Mathematics Subject Classification (2010):

• 54A25
• 54D10
• 54D25

Key words:

• Cardinal function
• S(n)-space
• θⁿ-closure
• S(n)-θ-closed
• quasi-Menger number

Notes

1 The research has been supported by the Program for State Aid of Leading RF Universities (Agreement No. 02.A03.21.0006 between the Ministry of Education and Science of the Russian Federation and the Ural Federal University, 27.08.2013).