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Section
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Mathematics
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Title
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On tightness and pseudocharacter of compact $T_1$-spaces
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Author(-s)
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Gryzlov A.A.a,
Golovastov R.A.a
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Affiliations
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Udmurt State Universitya
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Abstract
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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.
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Keywords
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$T_1$-space, compact, tightness, pseudocharacter
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UDC
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515.122.22, 515.122.252
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MSC
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54D10, 54D30
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DOI
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10.20537/vm190302
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Received
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15 July 2019
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Language
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Russian
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Citation
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Gryzlov A.A., Golovastov R.A. On tightness and pseudocharacter of compact $T_1$-spaces, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2019, vol. 29, issue 3, pp. 312-318.
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References
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