Glasnik Matematicki, Vol. 50, No. 1 (2015), 223-231.

ON PRODUCTS IN THE COARSE SHAPE CATEGORY

Tayyebe Nasri, Behrooz Mashayekhy and Hanieh Mirebrahimi

Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, P.O.Box 1159-91775, Mashhad, Iran
e-mail: ta_na8@stu-mail.um.ac.ir
e-mail: bmashf@um.ac.ir
e-mail: h_mirebrahimi@um.ac.ir


Abstract.   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 × 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.

2010 Mathematics Subject Classification.   55P55, 18A30.

Key words and phrases.   Coarse shape category, shape category, product.


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DOI: 10.3336/gm.50.1.13


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