Lusternik-Schnirelmann category and minimal coverings with contractible sets
type: Item
instance of: scholarly article
title: Lusternik-Schnirelmann category and minimal coverings with contractible sets
zbMATH Open document ID: 0643.55002
DOI: 10.1007/BF01169081
author: Mónica Clapp
author: L. Montejano
published in: Manuscripta Mathematica
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155209
review text: Let gcat(X) be the smallest number of contractible sets which cover a space X. The authors show that gcat(X) is not a homotopy invariant and the difference between gcat(X) and Lyusternik-Shnirelman category of X may be arbitrarily large. Theorem. For every positive integer n there are spaces \(K_ n\), \(X_ n\) and \(Y_ n\) with two points \(y_ 1,y_ 2\in Y_ n\) such that a) \(gcat(K_ n)-cat(K_ n)\geq n,\) b) \(gcat(X_ n)-gcat(X_ n\times [0,1])\geq n,\) c) \(gcat(Y_ n/\{y_ 1,y_ 2\})-gcat(Y_ n)\geq n\).
Mathematics Subject Classification ID: 55M30
Mathematics Subject Classification ID: 55R05
zbMATH DE Number: 4048654
zbMATH Keywords: Hurewicz fibration
zbMATH Keywords: geometric category
zbMATH Keywords: homotopy invariant
zbMATH Keywords: Lyusternik- Shnirelman category
MaRDI profile type: Publication
cites work: Invariants of the Lusternik-Schnirelmann Type and the Topology of Critical Sets
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cites work: Q3780112
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description: scientific article; zbMATH DE number 4048654