Version 1
: Received: 19 July 2024 / Approved: 19 July 2024 / Online: 19 July 2024 (16:57:43 CEST)
How to cite:
Kocinac, L. D. R.; Zaitov, A. A.; Eshimbetov, M. R. On \v{C}ech-Completeness of the Space of $\tau$-Smooth Idempotent Probability Measures. Preprints2024, 2024071612. https://doi.org/10.20944/preprints202407.1612.v1
Kocinac, L. D. R.; Zaitov, A. A.; Eshimbetov, M. R. On \v{C}ech-Completeness of the Space of $\tau$-Smooth Idempotent Probability Measures. Preprints 2024, 2024071612. https://doi.org/10.20944/preprints202407.1612.v1
Kocinac, L. D. R.; Zaitov, A. A.; Eshimbetov, M. R. On \v{C}ech-Completeness of the Space of $\tau$-Smooth Idempotent Probability Measures. Preprints2024, 2024071612. https://doi.org/10.20944/preprints202407.1612.v1
APA Style
Kocinac, L. D. R., Zaitov, A. A., & Eshimbetov, M. R. (2024). On \v{C}ech-Completeness of the Space of $\tau$-Smooth Idempotent Probability Measures. Preprints. https://doi.org/10.20944/preprints202407.1612.v1
Chicago/Turabian Style
Kocinac, L. D. R., Adilbek A. Zaitov and Muzaffar R. Eshimbetov. 2024 "On \v{C}ech-Completeness of the Space of $\tau$-Smooth Idempotent Probability Measures" Preprints. https://doi.org/10.20944/preprints202407.1612.v1
Abstract
For the set of probability measures ${\sf I}(X)$, where
$X$ is a compact Hausdorff space, we propose a new way to introduce
the topology by using open subsets of the space $X$. Then, among
other things, we give a new proof that for a compact Hausdorff
space $X$ the space ${\sf I}(X)$ is also a compact Hausdorff space.
For a Tychonoff space $X$, we consider the topological space ${\sf
I_{\tau}}(X)$ of $\tau$-smooth idempotent probability measures on
$X$,and show that the space ${\sf I_{\tau}}(X)$ is \v{C}ech-complete
if and only if the given space $X$ is \v{C}ech-complete.
Keywords
\v{C}ech-complete space; compact space; probability measure; $\tau$-smooth idempotent probability measure; neighbourhood system
Subject
Computer Science and Mathematics, Geometry and Topology
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
