Resolvability properties via independent families
type: Item
instance of: scholarly article
title: Resolvability properties via independent families
zbMATH Open document ID: 1110.54004
author: Wanjun Hu
author: W. W. Comfort
published in: Topology and its Applications
publication date: 2006-12-14T00:00:00Z
review text: For a given cardinal number \(\kappa > 1\), a topological space \(X\) is said to be \(\kappa\)-resolvable if it contains \(\kappa\) many pairwise disjoint dense subspaces. \(\Delta(X)\)-resolvable spaces are called maximally resolvable; here \(\Delta(X)\) is the dispersion character of \(X\), the minimal cardinality of a non-empty open subset of \(X\). \(X\) is extraresolvable if it contains a collection \(\mathcal D\) of dense subsets with \(| \mathcal D| = \Delta(X)^+\), such that the intersection of any two distinct elements of \(\mathcal D\) is nowhere dense in \(X\). This paper deals with the question of Juhász, Soukup and Szentmiklóssy if every extraresolvable Tychonoff space is maximally resolvable. Using some combinatorial principles the authors show that if GCH fails, there are extraresolvable not maximally resolvable Tychonoff spaces. It is also shown that a dense \(\omega\)-resolvable subspace of \(D(\lambda)^I\) is \(\lambda\)-resolvable.
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 03E05
Mathematics Subject Classification ID: 03E35
Mathematics Subject Classification ID: 05A18
Mathematics Subject Classification ID: 54A35
zbMATH DE Number: 5080165
zbMATH Keywords: \(\kappa\)-resolvable space
zbMATH Keywords: maximally resolvable space
zbMATH Keywords: extraresolvable space
zbMATH Keywords: independent family
reviewed by: Ljubiša D. R. Kočinac
MaRDI profile type: Publication
full work available at URL: j.topol.2006.02.005
OpenAlex ID: W2090339814
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DOI: 10.1016/J.TOPOL.2006.02.005
description: scientific article; zbMATH DE number 5080165