On products in the coarse shape categories

The paper is devoted to the study of coarse shape of Cartesian products of topological spaces. If the Cartesian product of two spaces \(X\) and \(Y\) admits an HPol-expansion, which is the Cartesian product of HPol-expansions of these spaces, then \(X\times Y\) is a product in the coarse shape categ...

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Bibliographic Details
Published inarXiv.org
Main Authors Nasri, Tayyebe, Mashayekhy, Behrooz, Mirebrahimi, Hanieh
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 28.07.2015
Subjects
Cartesian coordinates
Mathematics - Algebraic Topology
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Summary:The paper is devoted to the study of coarse shape of Cartesian products of topological spaces. If the Cartesian product of two spaces \(X\) and \(Y\) admits an HPol-expansion, which is the Cartesian product of HPol-expansions of these spaces, then \(X\times Y\) is a product in the coarse shape category. As a consequence, the Cartesian product of two compact Hausdorff spaces is a product in the coarse shape category. Finally, we show that the shape groups and the coarse shape groups commute with products under some conditions.
ISSN:2331-8422
DOI:10.48550/arxiv.1301.1641