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2 Bulletin of the Polish Academy of Sciences. Mathematics

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Movability and Uniform Movability of Shape Morphisms

Gevorgyan P. S., Pop I.

Bulletin of the Polish Academy of Sciences. Mathematics

2016

Vol. 64, no. 1

69--83

The purpose of this paper is to define some notions of movability for morphisms of inverse systems which extend the movability properties of inverse systems and which are compatible with the equivalence relations which define pro-morphisms and shape morphisms. Some properties and applications are given.

Uniformly movable categories and uniform movability of topological spaces

Gevorgyan P. S., Pop I.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

Vol. 55, no 3

229-242

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 horaotopy 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.