On Some Properties of Infinite Iterations of the Functor of Idempotent Probability Measures
A. A. ZaitovChirchik state pedagogical institute, 111700, Chirchik town, UzbekistanKh. F. KholturayevNational Research University Tashkent Institute of Irrigation and Agricultural Mechanization Engineers, 100000, Tashkent, Uzbekistan
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Abstract
In this article, we consider the sets $$I(X),P(X)\in\mathbb{R}^{C(X)}$$ , where $$I(X)$$ is the set of all idempotent probability measures on a compact Hausdorff space $$X$$ and $$P(X)$$ is the set of all probability measures equipped with the point-wise convergence topology. The uniform metrizability of the functor $$\mathcal{F}$$ of idempotent probability measures $$I$$ amd $$P$$ 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.
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