On Some Cardinal Properties of the Space $P_f(X)$ of Probability Measures

In this paper, given a compact space $X,$ we construct a continuous mapping from the space $P_f(X)$ of all probability measures on $X$ into the space of maximal linked systems of closed subsets of $X.$ Also, we investigate the behavior of the functional tightness and the local density of topological spaces under the action of the functor $P_f$: Comp→Comp. We show that the functor $P_f$ does not change the functional tightness and the local density of compact spaces.