On functional tightness and local density of the space of probability measures

In this paper, we study the behavior of the functional tightness and the local density of topological spaces under the influence of the functor of probability measures of finite support. It has been proved that the functor Pn preserves the functional tightness and the local density of compact spaces. Besides, a mapping from the special subspace P′(X) of probability measures into the space of maximal linked systems is constructed, and it is proved that this mapping is continuous.