On Some Cardinal Properties of the Space $P_f(X)$ of Probability Measures (Communications in Mathematical Research, 2024)
In this paper, given a compact space $X,$ we construct a continuousmapping from the space $P_f(X)$ of all probability measures on $X$ into the spaceof maximal linked systems of closed subsets of $X.$ Also, we investigate thebehavior of the functional tightness and the local density of topological spacesunder 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 compactspaces.
Keywords: Probability measure; functional tightness; local density; normal functor; superextension.