The Functor of Idempotent Probability Measures and Maps with Uniformity Properties of Uniform Spaces

Abstract

In the present paper we established that the functor of idempotent probability measures with a compact support transforms open maps into open maps and preserves the weight and the completeness index of uniform spaces. Consequently, the space of idempotent probability measures with a compact support is a locally compact Hausdorff space if and only if the original space is such.