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This article is cited in 4 scientific papers (total in 4 papers)
On Classes of Subcompact Spaces
V. I. Belugina, A. V. Osipovabc, E. G. Pytkeevab a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
c Ural State University of Economics, Ekaterinburg
Abstract:
This paper continues the study of P. S. Alexandroff's problem: When can a Hausdorff space $X$ be one-to-one continuously mapped onto a compact Hausdorff space? For a cardinal number $\tau$, the classes of $a_\tau$-spaces and strict $a_\tau$-spaces are defined. A compact space $X$ is called an $a_\tau$-space if, for any $C\in[X]^{\le\tau}$, there exists a one-to-one continuous mapping of $X\setminus C$ onto a compact space. A compact space $X$ is called a strict $a_\tau$-space if, for any $C\in[X]^{\le\tau}$, there exits a one-to-one continuous mapping of $X\setminus C$ onto a compact space $Y$, and this mapping can be continuously extended to the whole space $X$. In this paper, we study properties of the classes of $a_\tau$- and strict $a_\tau$-spaces by using Raukhvarger's method of special continuous paritions.
Keywords:
condensation, $a_\tau$-space, strict $a_\tau$-space, subcompact space, continuous partition, upper semicontinuous partition, ordered compact space, dyadic compact space.
Received: 28.06.2019 Revised: 10.03.2020
Citation:
V. I. Belugin, A. V. Osipov, E. G. Pytkeev, “On Classes of Subcompact Spaces”, Mat. Zametki, 109:6 (2021), 810–820; Math. Notes, 109:6 (2021), 849–858
Linking options:
https://www.mathnet.ru/eng/mzm12499https://doi.org/10.4213/mzm12499 https://www.mathnet.ru/eng/mzm/v109/i6/p810
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