Geodesic
Some Properties of Subcompact Spaces
Matematičeskie zametki, Tome 111 (2022) no. 2, pp. 188-201

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A Hausdorff topological space $X$ is said to be subcompact if it admits a coarser compact Hausdorff topology. P. S. Alexandroff asked the following question: What Hausdorff spaces are subcompact? A compact space $X$ is called a strict $a$-space if, for any $C\in [X]^{\le\omega}$, there exists a one-to-one continuous map of $X\setminus C$ onto a compact space $Y$ which can be continuously extended to the entire space $X$. The paper continues the study of classes of subcompact spaces. It is proved that the product of a compact space and a dyadic compact space without isolated points is a strict $a$-space.
Keywords: continuous bijection, $a$-space, strict $a$-space, subcompact space.
Mots-clés : condensation, dyadic compact space 
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     author = {V. I. Belugin and A. V. Osipov and E. G. Pytkeev},
     title = {Some {Properties} of {Subcompact} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {188--201},
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     number = {2},
     year = {2022},
     language = {ru},
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V. I. Belugin; A. V. Osipov; E. G. Pytkeev. Some Properties of Subcompact Spaces. Matematičeskie zametki, Tome 111 (2022) no. 2, pp. 188-201. http://geodesic.mathdoc.fr/item/MZM_2022_111_2_a1/