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

Annotatsiya

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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Identifikatorlar

DOI

10.1134/s1995080222110324

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