The existence of rigid measurable spaces
type: Item
instance of: scholarly article
title: The existence of rigid measurable spaces
zbMATH Open document ID: 0669.28001
DOI: 10.1016/0166-8641(89)90081-3
author: Manfred Droste
published in: Topology and its Applications
publication date: 1989-01-01T00:00:00Z
review text: For each uncountable cardinal \(\kappa\) the construction of \(2^{\kappa}\) linear orders \((S_ i,\leq)\) of cardinality \(\kappa\) is presented. Endowed with the order topology they have the following properties: they are pairwise nonembeddable into each other and the only embedding of \(S_ i\) into itself is the identity. If \(\kappa \geq \aleph_ 2\), then in each \(S_ i\) \(G_{\delta}\)-sets are open and hence the measurable spaces \((S_ i,{\mathcal B}_ i)\), where \({\mathcal B}_ i\) is the \(\sigma\)- algebra of all clopen subsets of \(S_ i\), are mono-rigid and pairwise nonembeddable into each other. Stationary sets control the character of points in \(S_ i's\). Some questions end the paper. (The reviewer has constructed a strongly rigid measurable space for \(\kappa =\aleph_ 1\), so the answer to one of them is known.)
Mathematics Subject Classification ID: 28A05
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 06A05
Mathematics Subject Classification ID: 54G10
zbMATH DE Number: 4095811
zbMATH Keywords: rigid linear order
zbMATH Keywords: order topology
zbMATH Keywords: Stationary sets
zbMATH Keywords: strongly rigid measurable space
MaRDI profile type: Publication
full work available at URL: 0166-8641(89)90081-3
OpenAlex ID: W2008316178
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description: scientific article; zbMATH DE number 4095811