Abstract:
In this article we consider covariant functors acting in the categorie of compacts, preserving the shapes of infinite compacts, $AN R$-systems, moving compacts, shape equivalence, homotopy equivalence and $A ( N ) SR$ properties of compacts. As well as shape properties of a compact space $X$ consisting of connectedness components $0$ of this compact $X$ under the action of covariant functors, are considered. And we study the shapes equality $ShX = ShY$ of infinite compacts for the space $P ( X )$ of probability measures and its subspaces.
Keywords:covariant functors, $A(N)R$-compacts, $ANR$-systems, probability measures, moving compacts, retracts, measures of finite support, shape equivalence, homotopy equivalence.
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