Intrinsic characterization of Alexander-Spanier cohomology groups of compactifications
type: Item
instance of: scholarly article
title: Intrinsic characterization of Alexander-Spanier cohomology groups of compactifications
zbMATH Open document ID: 1179.54026
published in: Topology and its Applications
publication date: 2009-08-20T00:00:00Z
review text: There is an ongoing interest in extensions and elaborations of the classical Alexander-Spanier cohomology theory, abbreviated here A-S. This paper provides several references with suitable historical annotations. The main impetus of this paper is to find an intrinsic characterization of the classical A-S cohomology groups of compactifications of completely regular spaces. Towards this end, an extension of A-S cohomology theory is given on the category of pairs of uniform spaces: This construction is functorial with values in the category of abelian groups satisfying the Eilenberg-Steenrod axioms. Moreover, this theory is precompact shape invariant and as desired it captures A-S cohomology groups of compactifications of completely regular spaces. Many related classical references and historical details are also provided.
Mathematics Subject Classification ID: 54C56
Mathematics Subject Classification ID: 54E15
Mathematics Subject Classification ID: 55N05
Mathematics Subject Classification ID: 55N40
Mathematics Subject Classification ID: 55P55
zbMATH DE Number: 5597512
zbMATH Keywords: uniform space
zbMATH Keywords: Alexander-Spanier cohomology theory
zbMATH Keywords: Eilenberg-Steenrod axioms
zbMATH Keywords: completion
zbMATH Keywords: compactification
zbMATH Keywords: uniform shape theory
author: Vladimir Baladze
reviewed by: Sukhjit Singh
MaRDI profile type: Publication
full work available at URL: j.topol.2009.01.023
OpenAlex ID: W2063404336
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DOI: 10.1016/J.TOPOL.2009.01.023
description: scientific article; zbMATH DE number 5597512