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

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.

85 pages, 1 figure. Section 13 reorganized. Section 13 also includes changes from errata cited as [23]