Bohr topologies and compact function spaces
type: Item
instance of: scholarly article
title: Bohr topologies and compact function spaces
zbMATH Open document ID: 1017.54021
DOI: 10.1016/S0166-8641(01)00269-3
author: Joan E. Hart
author: Kenneth Kunen
published in: Topology and its Applications
publication date: 2003-03-10T00:00:00Z
review text: Let \(\mathcal{U}\) be a structure for a countable language, and denote by \(\mathcal{U}^\sharp\) the structure \(\mathcal{U}\) with its Bohr topology. A compact structure \(\mathcal{X}\) is nice iff there is a single compact second countable structure \(\mathcal{R}\) such that the set of continuous homomorphisms from \(\mathcal{X}\) into \(\mathcal{R}\) separates the points of \(\mathcal{X}\). A structure \(\mathcal{U}\) (without a topology) is nice iff its Bohr compactification is nice. The authors show that a compact Hausdorff space \(Y\) is Eberlein compact iff \(Y\) is homeomorphic to some closed subspace of \(\mathcal{U}^\sharp\) for some nice \(\mathcal{U}\), and that \(Y\) is Talagrand compact iff \(Y\) is homeomorphic to a subspace of some \(\mathcal{U}^\sharp\).
Mathematics Subject Classification ID: 54H10
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 06B30
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 22A26
zbMATH DE Number: 1879118
zbMATH Keywords: Bohr topology
zbMATH Keywords: Eberlein compact
zbMATH Keywords: Talagrand compact
zbMATH Keywords: semilattice
zbMATH Keywords: structure
reviewed by: O. Gutik
MaRDI profile type: Publication
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full work available at URL: s0166-8641(01)00269-3
OpenAlex ID: W2063708298
description: scientific article; zbMATH DE number 1879118