CHARACTERIZATIONS OF STRONG

The purpose of this note is to give some characteriza tions by means of a special kind of normality of certain product topological spaces as well as by extension of con tinuous functions with values in normed linear spaces. Let us recall some notations and definitions. All topological spaces are assumed to be completely regular Hausdorff spaces. The topological space and its support are denoted with the same letter; for any subset A of a topological space X, A stands for the closure of A. For any set Y let A(Y) denote the Alexandrov's ( = one point) compactification of the discrete space of support Y. Definition 1. A topological space X is strongly col lectionwise Hausdorff if for any closed discrete subset F of X, there is a discrete family of open subsets of X, (UX)X€F ' such that x € Ux ' VX € F