# On infinite iterations of the functor of idempotent probability measures

## TL;DR

This paper proves that the functor of idempotent probability measures in the category of compacta is perfect metrizable, providing a significant topological property insight.

## Contribution

It establishes the perfect metrizability of the functor of idempotent probability measures in the category of compacta.

## Key findings

- The functor is perfect metrizable.
- Provides new topological insights into idempotent probability measures.
- Advances understanding of functor properties in topology.

## Abstract

In this paper we establish that the functor of idempotent probability measures acting in the category of compacta and their continous mappings is perfect metrisable