Movable morphisms in strong shape category
type: Item
instance of: scholarly article
title: Movable morphisms in strong shape category
zbMATH Open document ID: 1437.55015
author: Ioan Pop
author: P. S. Gevorkian
published in: Topology and its Applications
publication date: 2020-04-07T00:00:00Z
review text: Shape theory was introduced by K. Borsuk in the late 60s of the last century with the intention to overcome problems with the classification of spaces having bad local properties, for the study of which homotopy theory is not suitable. Later on \textit{S. Mardešić} in [Strong shape and homology. Berlin: Springer (2000; Zbl 0939.55007)] introduced strong shape theory as an intermediate theory between homotopy and shape theory. Although the classification of spaces induced by isomorphisms in the strong shape category SSh(Top) coincides with the shape type classification, this theory has remained interesting mostly because of the notion of coherent mappings which are essential in its definition. The notion of movability of metrizable compacta was introduced by K. Borsuk for the very first time. In their previous papers [Bull. Pol. Acad. Sci., Math. 64, No. 1, 69--83 (2016; Zbl 1353.55005); Topology Appl. 221, 309--325 (2017; Zbl 1373.55015)] and [\textit{I. Pop}, An. Ştiinţ. Univ. Al. I. Cuza Iaşi, Ser. Nouă, Mat. 59, No. 1, 25--42 (2013; Zbl 1324.54033)], the present authors have studied various types of movability for shape morphisms. In this work the authors use similar ideas to define movability properties for strong shape morphisms. First they consider a notion of movability of coherent mappings and after proving a series of technical statements they introduce a notion of movability of strong shape morphisms. They obtain some analogous results and give applications on strong shape equivalences between pointed topological spaces.
reviewed by: Nikola Koceić Bilan
Mathematics Subject Classification ID: 55P55
Mathematics Subject Classification ID: 54C56
zbMATH DE Number: 7187648
zbMATH Keywords: movable shape morphism
zbMATH Keywords: movable coherent morphisms
zbMATH Keywords: movable strong shape morphism
zbMATH Keywords: shape equivalence
zbMATH Keywords: weak shape equivalence
zbMATH Keywords: strong shape equivalence
zbMATH Keywords: coherent homotopy groups
zbMATH Keywords: strong shape weak equivalence
MaRDI profile type: Publication
full work available at URL: j.topol.2019.107001
OpenAlex ID: W2995141439
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Wikidata QID: Q126553478
DOI: 10.1016/J.TOPOL.2019.107001
description: scientific article; zbMATH DE number 7187648