On Some Properties of Infinite Iterations of the Functor of Idempotent Probability Measures

In this article, we consider the sets , where is the set of all idempotent probability measures on a compact Hausdorff space and is the set of all probability measures equipped with the point-wise convergence topology. The uniform metrizability of the functor of idempotent probability measures amd i...

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Veröffentlicht in:Lobachevskii journal of mathematics 2022-08, Vol.43 (8), p.2341-2348
Hauptverfasser: Zaitov, A. A., Kholturayev, Kh. F.
Format: Artikel
Sprache:eng
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Zusammenfassung:In this article, we consider the sets , where is the set of all idempotent probability measures on a compact Hausdorff space and is the set of all probability measures equipped with the point-wise convergence topology. The uniform metrizability of the functor of idempotent probability measures amd is studied. It is proved that the functor of idempotent probability measures, acting in the category of compact Hausdorff spaces and in their continuous mappings, is perfect metrizable.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080222110324