Abstract:
In this paper we define a numerical shape invariant of a continuous map called shape dimension of a map, which generalizes the shape dimension of a topological space. Some basic properties and applications of this invariant are given. The question of raising the shape dimension by shape finite-dimensional maps is solved. An example of a shape finite-dimensional surjective map between shape infinite-dimensional spaces is given.
Keywords and phrases:dimension of a morphism of inverse systems, of a pro-morphism, shape dimension of a shape morphism, of a map.
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