On the Čech-Completeness of the Space of τ-Smooth Idempotent Probability Measures

被引：0
|
作者：
Kocinac, Ljubisa D. R. [1 ,2 ]
Zaitov, Adilbek A. [3 ]
Eshimbetov, Muzaffar R. [4 ,5 ]
机构：
[1] Univ Nis, Fac Sci & Math, Nish 18000, Serbia
[2] State Univ Novi Pazar, Dept Math, Novi Pazar 36300, Serbia
[3] Tashkent Univ Architecture & Civil Engn, Dept Math & Nat Disciplines, Yangi Shahar Str 9, Tashkent 100194, Uzbekistan
[4] Uzbek Acad Sci, VI Romanovskiy Inst Math, Univ Str 9, Tashkent 100174, Uzbekistan
[5] Tashkent Int Univ Financial Management & Technol, Dept Math, Amir Temur Str 15, Tashkent 100047, Uzbekistan
来源：
AXIOMS | 2024年 / 13卷 / 08期
关键词：
& Ccaron; ech-complete space; compact space; probability measure; tau-smooth idempotent probability measure; neighbourhood system; FUNCTOR;
D O I：
10.3390/axioms13080569
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For the set I(X) of probability measures on a compact Hausdorff space X, we propose a new way to introduce the topology by using the open subsets of the space X. Then, among other things, we give a new proof that for a compact Hausdorff space X, the space I(X) is also a compact Hausdorff space. For a Tychonoff space X, we consider the topological space I-tau(X) of tau-smooth idempotent probability measures on X and show that the space I-tau(X) is & Ccaron;ech-complete if and only if the given space X is & Ccaron;ech-complete.
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页数：13
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