On the Steenrod homology theory of compact spaces
type: Item
instance of: scholarly article
title: On the Steenrod homology theory of compact spaces
zbMATH Open document ID: 0762.55002
author: Hvedri Inassaridze
published in: Michigan Mathematical Journal
publication date: 1992-09-27T00:00:00Z
review text: A new axiomatic characterization of the Steenrod homology on the category of all compact Hausdorff spaces is given. It is formulated in terms of bifunctor homology theory (homology group depends on both: space and coefficients) and is based on Eilenberg-Steenrod axioms. The characterization is very relevant to Eilenberg-Steenrod theorem on uniqueness of the Čech cohomology theory defined on all compact spaces. As a consequence author obtains the following proposition: A homology theory on the category of compact Hausdorff spaces is isomorphic to the Steenrod homology theory if and only if it is an exact theory which is isomorphic to the Čech theory for every infinitely divisible abelian group.
Mathematics Subject Classification ID: 55N07
zbMATH DE Number: 59877
zbMATH Keywords: Steenrod homology
zbMATH Keywords: compact Hausdorff spaces
zbMATH Keywords: Eilenberg-Steenrod axioms
zbMATH Keywords: Čech cohomology
reviewed by: Alexander Dranishnikov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029004385
OpenAlex ID: W2035469161
DOI: 10.1307/MMJ/1029004385
description: scientific article; zbMATH DE number 59877