Homogeneity and \(\pi\)-networks
type: Item
instance of: scholarly article
title: Homogeneity and \(\pi\)-networks
zbMATH Open document ID: 0708.54017
author: D. B. Motorov
published in: Moscow University Mathematics Bulletin
publication date: 1989-01-01T00:00:00Z
review text: Let \(B_ 0\) be the class of all zero-dimensional bicompacta of a countable character and let \(B_ 1\) be the class of all linearly ordered continua of a countable character. A space \(X\in B_ 0\) \((X\in B_ 1)\) is said to be h-homogeneous (l-homogeneous) if any two nonempty clopen subsets (nonsingle-point subsegments) of X are homeomorphic (similar). Except for a certain reinforcement of a former result of the author concerning the homogeneity of a space \(X\in B_ 0\) homogeneity properties of products of spaces from the mentioned classes are investigated. For example, if \(\alpha\) is the class of representatives of \(B_ 0\) with respect to the equivalence given by homeomorphism and \(\beta =\{X\in \alpha\); X is homogeneous\(\}\) then the spaces \(\Pi\alpha\) and \(\Pi\beta\) are homeomorphic.
reviewed by: J. Chvalina
Mathematics Subject Classification ID: 54D30
Mathematics Subject Classification ID: 54E15
Mathematics Subject Classification ID: 54E20
Mathematics Subject Classification ID: 54C99
zbMATH DE Number: 4163703
zbMATH Keywords: zero-dimensional bicompacta of a countable character
zbMATH Keywords: linearly ordered continua
zbMATH Keywords: homogeneous space
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4163703