Ideal resolvability
type: Item
instance of: scholarly article
title: Ideal resolvability
zbMATH Open document ID: 0955.54001
DOI: 10.1016/S0166-8641(97)00257-5
author: K. Appert
published in: Topology and its Applications
publication date: 2001-02-21T00:00:00Z
review text: A~nonempty topological space is resolvable if it contains two disjoint dense subsets. Let \(\mathcal I\) be an ideal of sets in a~topological space \((X,\tau)\). A~set \(A\subseteq X\) is \(\mathcal I\)-dense if for every \(x\in X\) and every open neighbourhood~\(U\) of~\(x\), \(U\cap A\notin\mathcal I\). A~topological space is \(\mathcal I\)-resolvable if it contains two disjoint \(\mathcal I\)-dense subsets. It is maximal \(\mathcal I\)-resolvable if it is \(\mathcal I\)-resolvable and no strictly finer topology is \(\mathcal I\)-resolvable. These and related notions are investigated in the paper. In particular, the resolvability of the density topology is proved.
reviewed by: Miroslav Repický
Mathematics Subject Classification ID: 54A05
Mathematics Subject Classification ID: 54H05
Mathematics Subject Classification ID: 28A05
Mathematics Subject Classification ID: 54G99
zbMATH DE Number: 1307867
zbMATH Keywords: topological ideal
zbMATH Keywords: resolvable space
zbMATH Keywords: \(\mathcal I\)-dense set
MaRDI profile type: Publication
full work available at URL: s0166-8641(97)00257-5
OpenAlex ID: W4210545353
Wikidata QID: Q127011498
Recommended article: Q4229110
Recommended article: Resolvability vs. almost resolvability
Recommended article: Maximal minimal resolutions
Recommended article: Q4907395
Recommended article: Completeness of resolution revisited
Recommended article: On complete resolutions
Recommended article: Q4955943
Recommended article: A note on resolvability
Recommended article: Resolvable configurations
Recommended article: Generalizing resolution
description: scientific article; zbMATH DE number 1307867