On the Čech-Completeness of the Space of τ-Smooth Idempotent Probability Measures
Ljubiša D. R. KočinacDepartment of Mathematics, State University of Novi Pazar, 36300 Novi Pazar, SerbiaA. A. ZaitovDepartment of Mathematics and Natural Disciplines, Tashkent University of Architecture and Civil Engineering, Yangi Shahar Str. 9, Tashkent 100194, UzbekistanMuzaffar R. EshimbetovDepartment of Mathematics, Tashkent International University of Financial Management and Technology, Amir Temur Str. 15, Tashkent 100047, Uzbekistan
ABI
Аннотация
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 Iτ(X) of τ-smooth idempotent probability measures on X and show that the space Iτ(X) is Čech-complete if and only if the given space X is Čech-complete.
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