Matematicheskie Zametki
 RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 2021, Volume 109, Issue 6, Pages 810–820 (Mi mz12499)

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.
* Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm12499

Full text: PDF file (516 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Mathematical Notes, 2021, 109:6, 849–858

Bibliographic databases:

UDC: 515.122.5
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

Citation in format AMSBIB
\Bibitem{BelOsiPyt21} \by V.~I.~Belugin, A.~V.~Osipov, E.~G.~Pytkeev \paper On Classes of Subcompact Spaces \jour Mat. Zametki \yr 2021 \vol 109 \issue 6 \pages 810--820 \mathnet{http://mi.mathnet.ru/mz12499} \crossref{https://doi.org/10.4213/mzm12499} \transl \jour Math. Notes \yr 2021 \vol 109 \issue 6 \pages 849--858 \crossref{https://doi.org/10.1134/S0001434621050187} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000670513000018} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85118133732}