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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2019, Volume 29, Issue 3, Pages 312–318 (Mi vuu684)  

MATHEMATICS

On tightness and pseudocharacter of compact $T_1$-spaces

A. A. Gryzlov, R. A. Golovastov

Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia

Abstract: We consider the relationship between the pseudocharacter $\psi(X)$ and the tightness $t(X)$ of compact $T_1$-spaces $X$. We prove that $t(X)\leqslant\psi(X)$ for self-adjoined $T_1$-spaces, i.e., the spaces where a subset is closed if and only if it is compact. We also show that in general for compact $T_1$-spaces there is no relationship between these cardinal invariants. We give an example of a compact $T_1$-space such that the tightness of this space is uncountable, but its pseudocharacter is countable. Another example shows the space $X$ whose tightness is countable, but its pseudocharacter is uncountable.

Keywords: $T_1$-space, compact, tightness, pseudocharacter.

Funding Agency Grant Number
Ministry of Science and Higher Education of the Russian Federation 1.5211.2017/8.9
The research was supported by the Ministry of Science and Higher Education of the Russian Federation in the framework of the basic part (project no. 1.5211.2017/8.9).


DOI: https://doi.org/10.20537/vm190302

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Full text: http://vm.udsu.ru/.../2019-3-2
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Bibliographic databases:

UDC: 515.122.22, 515.122.252
MSC: 54D10, 54D30
Received: 15.07.2019

Citation: A. A. Gryzlov, R. A. Golovastov, “On tightness and pseudocharacter of compact $T_1$-spaces”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 29:3 (2019), 312–318

Citation in format AMSBIB
\Bibitem{GryGol19}
\by A.~A.~Gryzlov, R.~A.~Golovastov
\paper On tightness and pseudocharacter of compact $T_1$-spaces
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2019
\vol 29
\issue 3
\pages 312--318
\mathnet{http://mi.mathnet.ru/vuu684}
\crossref{https://doi.org/10.20537/vm190302}


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  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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