On a problem for spaces of the first category
type: Item
instance of: scholarly article
title: On a problem for spaces of the first category
zbMATH Open document ID: 0614.54027
published in: Moscow University Mathematics Bulletin
publication date: 1986-01-01T00:00:00Z
review text: It is proved that every metric space of first category having the property that the weight of each nonvoid open subset is at least a cardinal k, contains as a closed subspace a homeomorph of the small \(\sigma\)-product of countably many discrete spaces of cardinality k (in fact, a more general result for regular spaces is proved). Another result shows that a metric space is of first category iff it contains a \(\sigma\)-discrete dense \(g_{\delta}\)-set having no isolated point. At the end, several results without proofs are stated dealing with special types of homogenities.
Mathematics Subject Classification ID: 54E52
zbMATH DE Number: 3994530
zbMATH Keywords: metric space of first category
zbMATH Keywords: weight
zbMATH Keywords: closed subspace
zbMATH Keywords: \(\sigma \)- discrete dense \(g_{\delta }\)-set
zbMATH Keywords: no isolated point
author: S. V. Medvedev
reviewed by: M. Hušek
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3994530