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Volume 40, Issue 4
On Some Cardinal Properties of the Space $P_f(X)$ of Probability Measures

Shavkat Ayupov & Nodirbek Mamadaliev

DOI: 10.4208/cmr.2024-0036

Commun. Math. Res., 40 (2024), pp. 383-399.

Published online: 2024-12

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  • Abstract

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.

  • Keywords

Probability measure, functional tightness, local density, normal functor, superextension.

  • AMS Subject Headings

18A22, 18B30, 46E27, 46J10, 54C35

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CMR-40-383, author = {Ayupov , Shavkat and Mamadaliev , Nodirbek}, title = {On Some Cardinal Properties of the Space $P_f(X)$ of Probability Measures}, journal = {Communications in Mathematical Research }, year = {2024}, volume = {40}, number = {4}, pages = {383--399}, abstract = {

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.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2024-0036}, url = {http://global-sci.org/intro/article_detail/cmr/23698.html} }
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 -

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.

Ayupov , Shavkat and Mamadaliev , Nodirbek. (2024). On Some Cardinal Properties of the Space $P_f(X)$ of Probability Measures. Communications in Mathematical Research . 40 (4). 383-399. doi:10.4208/cmr.2024-0036
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