Countable dense homogeneity and the Baire property
type: Item
instance of: scholarly article
title: Countable dense homogeneity and the Baire property
zbMATH Open document ID: 0780.54029
DOI: 10.1016/0166-8641(92)90148-S
author: Ben jun. Fitzpatrick
author: Hao-Xuan Zhou
published in: Topology and its Applications
publication date: 1992-09-27T00:00:00Z
review text: A separable space \(X\) is called countable dense homogeneous (CDH) if for all countable dense subsets \(A\) and \(B\) of \(X\) there is an autohomeomorphism \(h\) of \(X\) with \(h[A]=B\). In this paper the authors discuss countable dense homogeneity in relation with the Baire property. They show among other things that it is consistent with ZFC that every CDH metric space \(X\) of cardinality \({\mathfrak c}\) is nonmeager. They also show that under CH there is a meager CDH subspace of the real line. Hence it is independent with ZFC that there is a meager CDH metric space of size \({\mathfrak c}\).
reviewed by: Jan van Mill
Mathematics Subject Classification ID: 54E52
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 54A35
zbMATH DE Number: 60701
zbMATH Keywords: meager countable dense homogeneous metric space
zbMATH Keywords: countable dense homogeneity
MaRDI profile type: Publication
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cites work: Countable dense homogeneous spaces under Martin's axiom
cites work: Q3220578
cites work: Countable dense homogeneous spaces
cites work: Derivatives on countable dense subsets
cites work: A note on countable dense homogeneity
cites work: Q3774544
cites work: Q3833238
cites work: Conditions under which a connected representable space is locally connected
cites work: Homogeneity of infinite products of manifolds with boundary
cites work: Mapping a set of reals onto the reals
cites work: Q3715868
cites work: Homeomorphisms of Manifolds with Prescribed Behaviour on Large Dense Sets
cites work: Countable dense homogeneity and n-homogeneity
cites work: Strong Local Homogeneity Does not Imply Countable Dense Homogeneity
cites work: Q4030161
cites work: Q3805437
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description: scientific article; zbMATH DE number 60701