COVARIANT FUNCTORS AND THE SHAPES IN THE CATEGORY OF COMPACTS

In this note, we consider covariant functors acting in the categorie of com-pacts, preserving the shapes of infinite compacts, -systems, moving compacts, shape equi-valence, homotopy equivalence and properties of compacts. As well as, shape pro-perties of a compact spaceconsisting of connectedness components ⧠Х of this compact under the action of covariant functors, are considered. And as we study the shapes equality of infinite compacts for the space of probability measures and its subspa-ces.