Uniformly finer topologies
type: Item
instance of: scholarly article
title: Uniformly finer topologies
zbMATH Open document ID: 0882.54001
DOI: 10.1007/BF02844515
publication date: 1997-11-19T00:00:00Z
review text: The author gives examples of metric \((\sigma\)-compact, Polish, complete and locally compact) spaces \((X,\tau)\) which admit a topology \(\tau'\), uniformly finer than the topology \(\tau\), such that \((X,\tau')\) and \((X,\tau)\) are homeomorphic. He shows that for \(\sigma\)-compact Čech-complete spaces this cannot happen. Further he shows that for homeomorphic metric spaces \((X,\tau)\) and \((X,\tau')\) where \(\tau'\) is uniformly finer than \(\tau\), there exists a nonregular topology \(\tau''\) on \(X\) such that \(\tau \subset \tau'' \subset \tau'\).
reviewed by: Bernhard Behrens
Mathematics Subject Classification ID: 54A10
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 1089787
zbMATH Keywords: uniformly finer topology
zbMATH Keywords: \(\sigma\)-compact Čech-complete spaces
zbMATH Keywords: homeomorphic metric spaces
author: J. M. Aldaz
MaRDI profile type: Publication
cites work: Q5541832
full work available at URL: https://doi.org/10.1007/bf02844515
OpenAlex ID: W2079006441
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 1089787