Some generalizations of the concept of a \(p\)-space
type: Item
instance of: scholarly article
title: Some generalizations of the concept of a \(p\)-space
zbMATH Open document ID: 1229.54036
author: A. V. Arhangel'skii
author: Mitrofan M. Choban
published in: Topology and its Applications
publication date: 2011-08-04T00:00:00Z
review text: The authors define generalizations of the notion of a \(p\)-space. We say that a subset~\(X\) of a space~\(Z\) is \(s\)-embedded if there is a countable family~\(\mathcal S\) of open subsets such that \(X\)~can be written as the union of a family of subsets, each of which is the intersection of a subfamily of~\(\mathcal S\). An \(s\)-space is one which is \(s\)-embedded in one of its compactifications. A partial pluming of~\(X\) in~\(Z\) is a sequence \(\langle\gamma_n:n\in\omega\rangle\) of families of open sets such that whenever \(x\in X\) and \(z\in Z\setminus X\) there is an~\(n\) such that \(x\in\bigcup\gamma_n\) and \(z\notin\text{St}(x,\gamma_n)\); the sequence is a pluming if \(X\subset\bigcup\gamma_n\) for all~\(n\). If \(X\)~has a (partial) pluming in~\(Z\) then it is said to be \(p\)-embedded (\(p^*\)-embedded) in~\(Z\); a \(p\)-space (\(p^*\)-space) is one that is \(p\)-embedded (\(p^*\)-embedded) in some compactification. Besides establishing the basic properties of and the relations between these notions the authors also apply them to sufficient conditions for and characterizations of being a \(p\)-space or metrizable.
Mathematics Subject Classification ID: 54E18
Mathematics Subject Classification ID: 54D20
zbMATH DE Number: 5935885
zbMATH Keywords: \(p\)-space
zbMATH Keywords: \(p^*\)-space
zbMATH Keywords: \(s\)-space
zbMATH Keywords: Borel set
zbMATH Keywords: pseudocompact space
reviewed by: K. P. Hart
MaRDI profile type: Publication
full work available at URL: j.topol.2011.05.012
OpenAlex ID: W2001887287
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DOI: 10.1016/J.TOPOL.2011.05.012
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description: scientific article; zbMATH DE number 5935885