TY - JOUR
T1 - On Some Cardinal Properties of the Space $P_f(X)$ of Probability Measures
AU - Ayupov , Shavkat
AU - Mamadaliev , Nodirbek
JO - Communications in Mathematical Research 
VL - 4
SP - 383
EP - 399
PY - 2024
DA - 2024/12
SN - 40
DO - http://doi.org/10.4208/cmr.2024-0036
UR - https://global-sci.org/intro/article_detail/cmr/23698.html
KW - Probability measure, functional tightness, local density, normal functor, superextension.
AB - <p style="text-align: justify;">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 $P_f$: <em>Comp</em>→<em>Comp</em>. We show that the functor $P_f$ does not change the functional tightness and the local density of compact
spaces.</p>