Uniformly Movable Categories and Uniform Movability of Topological Spaces

P. S. Gevorgyan¹ ; I. Pop²

¹ Department of Higher Mathematics Moscow Power Engineering Institute (Technical University) Krasnokazarmennaya, 14 111250 Moscow, Russia
² Faculty of Mathematics “Al. I. Cuza” University 700505 Iaşi, Romania

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) no. 3, pp. 229-242

Résumé

A categorical generalization of the notion of movability from inverse systems and shape theory was given by the first author who defined the notion of movable category and used it to interpret the movability of topological spaces. In this paper the authors define the notion of uniformly movable category and prove that a topological space is uniformly movable in the sense of shape theory if and only if its comma category in the homotopy category HTop over the subcategory HPol of polyhedra is uniformly movable. This is a weakened version of the categorical notion of uniform movability introduced by the second author.

Détail

DOI : 10.4064/ba55-3-5

Keywords: categorical generalization notion movability inverse systems shape theory given first author who defined notion movable category interpret movability topological spaces paper authors define notion uniformly movable category prove topological space uniformly movable sense shape theory only its comma category homotopy category htop subcategory hpol polyhedra uniformly movable weakened version categorical notion uniform movability introduced second author