On the Preservation of Projective Limits by Functors of Non-Deterministic, Probabilistic, and Mixed Choice

TL;DR

This paper investigates the preservation of projective limits in topological spaces through various functors representing probabilistic, non-deterministic, and mixed choices, identifying conditions for their preservation.

Contribution

It provides new insights into how different functors related to probabilistic and non-deterministic choice preserve projective limits in topological spaces.

Findings

Identifies conditions under which functors preserve projective limits.

Analyzes preservation properties for multiple functors including valuation and hyperspace functors.

Enhances understanding of the interplay between topology and computational effects.

Abstract

We examine conditions under which projective limits of topological spaces are preserved by the continuous valuation functor $\mathbf V$ and its subprobability and probability variants (used to represent probabilistic choice), by the Smyth hyperspace functor (demonic non-deterministic choice), by the Hoare hyperspace functor (angelic non-deterministic choice), by Heckmann's $\mathbf A$-valuation functor, by the quasi-lens functor, by the Plotkin hyperspace functor (erratic non-deterministic choice), and by prevision functors and powercone functors that implement mixtures of probabilistic and non-deterministic choice.