Functional characterizations of certain p-spaces
type: Item
instance of: scholarly article
title: Functional characterizations of certain p-spaces
zbMATH Open document ID: 0564.54013
DOI: 10.1016/0166-8641(85)90076-8
author: J. Blot
published in: Topology and its Applications
publication date: 1985-01-01T00:00:00Z
review text: The authors prove the following theorem. A completely regular space Y is a p-space (respectively, a Čech-complete space) with a \(G_{\delta}\)-diagonal iff given a dense subspace A of any space X and a continuous \(f: A\to Y\) there is a p-embedded subset (resp. a \(G_{\delta}\)-subset) M of X which contains A and a continuous \(\hat f:\) \(M\to Y\) which extends f. This generalizes the well-known analogous result for completely metrizable spaces.
Mathematics Subject Classification ID: 54E18
Mathematics Subject Classification ID: 54C20
Mathematics Subject Classification ID: 54E50
zbMATH DE Number: 3899729
zbMATH Keywords: completely regular space
zbMATH Keywords: p-space
zbMATH Keywords: Čech-complete space
zbMATH Keywords: \(G_{\delta }\)-diagonal
reviewed by: Sheldon W. Davis
MaRDI profile type: Publication
full work available at URL: 0166-8641(85)90076-8
OpenAlex ID: W2050436849
cites work: On p-spaces and \(w\Delta\)-spaces
cites work: A nondevelopable locally compact hausdorff space with a Gδ-diagonal
cites work: Some generalizations of metric spaces
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description: scientific article; zbMATH DE number 3899729