Tychonoff expansions in which a given set is open
type: Item
instance of: scholarly article
title: Tychonoff expansions in which a given set is open
zbMATH Open document ID: 1031.54009
DOI: 10.1016/S0166-8641(02)00296-1
author: Wanjun Hu
published in: Topology and its Applications
publication date: 2003-07-29T00:00:00Z
review text: Let \((X,\tau)\) be a Tikhonov space without isolated points. There is a finer Tikhonov topology \(\tau'\) without isolated points containing a given dense-in-itself set \(A\) such that \(\tau'|A=\tau|A\) if and only if \(A\) does not intersect the closure of the set of isolated points of \(X\setminus A\). The possibility to find a Tikhonov dense-in-itself expansion \(\tau'\) of \(\tau\) that satisfies just \(A\in\tau'\) (or just \(\text{int}_{\tau'} A=\text{int}_{\tau} A\) instead) is also characterized.
Mathematics Subject Classification ID: 54C50
Mathematics Subject Classification ID: 54F65
Mathematics Subject Classification ID: 54B99
zbMATH DE Number: 1955989
zbMATH Keywords: Tikhonov expansion
zbMATH Keywords: dense-in-itself sets
reviewed by: Petr Holický
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1955989