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Acta Mathematica Hungarica

, Volume 159, Issue 1, pp 229–245 | Cite as

Cardinal inequalities for S(n)-spaces

  • I. S. GotchevEmail author
Article

Abstract

Hajnal and Juhász [9] proved that if X is a T1-space, then \({|X| \leq 2^{s(X)\psi(X)}}\), and if X is a Hausdorff space, then \({|X| \leq 2^{c(X)\chi(X)}}\) and \({|X| \leq 2^{2^{s(X)}}}\). Schröder sharpened the first two estimations by showing that if X is a Hausdorff space, then \({|X| \leq 2^{Us(X)\psi_c(X)}}\), and if X is a Urysohn space, then \({|X| \leq 2^{Uc(X)\chi(X)}}\).

In this paper, for any positive integer n and some topological spaces X, we define the cardinal functions \({\chi_n(X), \psi_n(X), s_n(X)}\), and cn(X) called respectively S(n)-character, S(n)-pseudocharacter, S(n)-spread, and S(n)-cellularity and using these new cardinal functions we show that the above-mentioned inequalities could be extended to the class of S(n)-spaces. We recall that the S(1)-spaces are exactly the Hausdorff spaces and the S(2)-spaces are exactly the Urysohn spaces.

Key words and phrases

cardinal function S(n)-space S(n)-character S(n)-pseudocharacter S(n)-discrete S(n)-spread S(n)-cellularity 

Mathematics Subject Classification

primary 54A25 54D10 

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Notes

Acknowledgement

The author is grateful to the anonymous referee for very careful reading of the paper and for several valuable suggestions.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesCentral Connecticut State UniversityNew BritainUSA

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