Geodesic
On tightness and pseudocharacter of compact $T_1$-spaces
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 29 (2019) no. 3, pp. 312-318

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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.
Keywords: $T_1$-space, compact, tightness, pseudocharacter. 
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     author = {A. A. Gryzlov and R. A. Golovastov},
     title = {On tightness and pseudocharacter of compact $T_1$-spaces},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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     publisher = {mathdoc},
     volume = {29},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2019_29_3_a1/}
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A. A. Gryzlov; R. A. Golovastov. On tightness and pseudocharacter of compact $T_1$-spaces. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 29 (2019) no. 3, pp. 312-318. http://geodesic.mathdoc.fr/item/VUU_2019_29_3_a1/