Strong homology and dimension
type: Item
instance of: scholarly article
title: Strong homology and dimension
zbMATH Open document ID: 0648.55006
DOI: 10.1016/0166-8641(88)90074-0
published in: Topology and its Applications
publication date: 1988-01-01T00:00:00Z
review text: Sei \(H_*(X;G)\) die von Lisica und Mardešić eingeführte starke Homologie für einen beliebigen Raum X und beliebige abelsche Koeffizientengruppe G. Die Autoren zeigen: 1) Für \(p>sd X\) \((=shape\) Dimension von X) verschwindet \(H_ p(X;G)\). 2) Es gibt eindimensionale Räume, die aber keine ANR Auflösung aus eindimensionalen Räumen besitzen. Letzteres Ergebnis zeigt, daß die Aussage 1) nicht trivial über die Dimension von ANR Auflösungen gefolgert werden kann. Das Ergebnis 1) verschärft bekannte Resultate über starke (im Gegensatz z.B. zur singulären) Homologie.
Mathematics Subject Classification ID: 55N07
Mathematics Subject Classification ID: 55P55
Mathematics Subject Classification ID: 54F45
Mathematics Subject Classification ID: 54B35
zbMATH DE Number: 4058424
zbMATH Keywords: strong shape theory
zbMATH Keywords: shape dimension
zbMATH Keywords: strong homology
zbMATH Keywords: ANR-resolutions by 1-dimensional spaces
author: Sibe Mardešić
author: Tadashi Watanabe
reviewed by: Friedrich Wilhelm Bauer
MaRDI profile type: Publication
full work available at URL: 0166-8641(88)90074-0
OpenAlex ID: W2051152334
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description: scientific article; zbMATH DE number 4058424