(untitled) (Communications in Mathematical Research, 2024)
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.