A remainder for some non-locally compact spaces
type: Item
instance of: scholarly article
title: A remainder for some non-locally compact spaces
zbMATH Open document ID: 0877.54021
author: Yusuf Ünlü
author: Fikret Kuyucu
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1997-12-10T00:00:00Z
review text: All spaces considered are completely regular and Hausdorff. A subset \(F\) of a space \(X\) has countable character if there is a sequence of open sets \(V_1\supseteq V_2\supseteq\dots \supseteq F\) such that if \(V\) is open in \(X\) and \(F\subseteq V\) then there is an \(n\) for which \(V_n\subseteq V\). The residue \(R(X)\) of \(X\) is the set of points in \(X\) which do not possess compact neighbourhoods. It was shown by \textit{R. E. Chandler} and \textit{F.-C. Tzung} [Proc. Am. Math. Soc. 70, 196-202 (1978; Zbl 0419.54011)] that if \(X\) is real compact, \(R(X)= \{p\}\) and \(p\) is contained in a compact set of countable character, then \([0,1)\) is a remainder of \(X\). In the current paper, the authors provide a partial generalization of this result. To that end, \(T_n\) is defined as the set of points in \(\mathbb{R}^n\) on the positive coordinate axes whose distance to the origin is less than or equal to 1, \(\{e_1,\dots, e_n\}\) as the endpoints of \(T_n\) and \(T_n^0= T_n-\{e_1, e_2,\dots, e_n\}\). The major result is Theorem 7: Let \(X\) be realcompact and \(R(X)= \{p_1,\dots,p_n\}\). If \(R(X)\) has countable character then \(T_n^0\) is a remainder of \(X\).
Mathematics Subject Classification ID: 54D40
zbMATH DE Number: 955226
zbMATH Keywords: compactification
zbMATH Keywords: remainder
zbMATH Keywords: countable character
reviewed by: James Hatzenbuhler
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 955226