# On $C$-properties of the space of idempotent robability measures

## TL;DR

This paper investigates the topological properties of the space of idempotent probability measures, showing it inherits kappa-metrizability from the underlying space and analyzing the behavior of associated functors.

## Contribution

It establishes kappa-metrizability transfer for idempotent probability measures and constructs max-plus-convex subfunctors, advancing the understanding of their topological and functorial properties.

## Key findings

- The space of idempotent probability measures is kappa-metrizable if the underlying space is.
- Constructed a series of max-plus-convex subfunctors of the idempotent probability measures functor.
- The functor preserves openness of continuous maps.

## Abstract

In the work it is shown that the space of idempotent probability measures with compact supports is kappa-metrizable if the given Tychonoff space is kappa-metrizable. It is constructed a series of max-plus-convex subfunctors of the functor of idempotent probability measures with compact supports. Further, it is established that the functor of idempotent probability measures with the compact supports preserves openness of continuous maps.