On power homogeneous spaces
type: Item
instance of: scholarly article
title: On power homogeneous spaces
zbMATH Open document ID: 0994.54028
DOI: 10.1016/S0166-8641(01)00130-4
published in: Topology and its Applications
publication date: 2002-08-22T00:00:00Z
review text: A topological space \(X\) is called power homogeneous if there exists a cardinal number \(\tau>0\) such that the space \(X^\tau\) is homogeneous. It may easily happen that a space \(X\) is not homogeneous while \(X\) is power homogeneous. Every first countable zero-dimensional Hausdorff space is \(\omega\)-power homogeneous. In this paper, some new necessary conditions for a space to be power homogeneous are obtained. The notions of a Moscow space and a weakly Klebanov space are applied to study power homogeneous spaces. In particular it is proved that (1) every Corson compact power homogeneous space is first countable; (2) a compact scattered space is power homogeneous if and only if it is countable.
Mathematics Subject Classification ID: 54D50
Mathematics Subject Classification ID: 54D60
Mathematics Subject Classification ID: 54C35
zbMATH DE Number: 1787547
zbMATH Keywords: homogeneity
zbMATH Keywords: Corson compact space
zbMATH Keywords: Moscow space
zbMATH Keywords: weakly Klebanov space
zbMATH Keywords: scattered space
author: A. V. Arhangel'skii
reviewed by: Shou Lin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1787547