Clean-cut pairs (F(X), ηF (X)) compacts of type F(X).

In this paper, studying the location of compact sets in each other, we consider sharply defined (cc-pairs) pairs (P(X), ηP (X)) for the functor P : Comp → Comp-probability measures in the category of compact sets and continuous self-mappings [1, 2]. It is proved that for any closed subset A ⊂ X different from X, subspaces of the space P(X) of the form P(A), ηPf (X) and ηPf, n (X) form sharply defined pairs of the compact set P (X). pairs (P(X), P(A)), (Pf (X), ηPf (X)) and (Pf, n(X), ηPf, n (X)) a re clean-cut (briefly, cc-pairs) of P (X). In addition, homotopy dense subspaces P(X) of all probability measures defined in an infinite compact set X are singled out. It is also shown that for any infinite convex compact set X, the pair (P(X), ηP (X)) is a clean-cut pair. [ABSTRACT FROM AUTHOR]