A class of compact subsets for non-sober topological spaces

TL;DR

This paper introduces a new class of subsets in topological spaces that generalizes compact saturated sets in sober spaces and retains useful properties in non-sober spaces, with applications to capacity theory.

Contribution

It defines a novel class of subsets that unify properties across sober and non-sober spaces, enhancing the theoretical framework for capacity theory.

Findings

The class coincides with compact saturated sets in sober spaces.

It maintains desirable properties in non-sober spaces.

Applications to capacity theory are explored.

Abstract

We define a class of subsets of a topological space that coincides with the class of compact saturated subsets when the space is sober, and with enough good properties when the space is not sober. This class is introduced especially in view of applications to capacity theory.