Remarks to the Vietoris theorem
type: Item
instance of: scholarly article
title: Remarks to the Vietoris theorem
zbMATH Open document ID: 0891.55024
DOI: 10.12775/TMNA.1996.041
author: Wojciech Kryszewski
published in: Topological Methods in Nonlinear Analysis
publication date: 1998-07-12T00:00:00Z
review text: The author considers extensions of the classical theorem of \textit{L. Vietoris} [Math. Ann. 97, 454-472 (1927; JFM 53.0552.01)] giving homology conditions on the fibres of a surjective map \(f:X\rightarrow Y\) which insure that \(f\) induces an isomorphism in homology. A survey of the literature is given and some homotopy and cohomotopy versions of Vietoris' theorem are established e.g. conditions on a space \(P\) and map \(f:X\rightarrow Y\) are given insuring that \(f^*:[Y,P]\rightarrow [X,P]\) is bijective. The proofs are by classical obstruction theory.
Mathematics Subject Classification ID: 55S37
Mathematics Subject Classification ID: 55N20
Mathematics Subject Classification ID: 55M20
Mathematics Subject Classification ID: 55Q20
zbMATH DE Number: 1127706
zbMATH Keywords: Vietoris theorem
zbMATH Keywords: cohomotopy
zbMATH Keywords: infinite-dimensional stable cohomotopy
zbMATH Keywords: JFM 53.0552.01
reviewed by: Keith Johnson
MaRDI profile type: Publication
full work available at URL: tmna.1996.041
OpenAlex ID: W2583433014
description: scientific article; zbMATH DE number 1127706