Semisolid sets and topological measures

This paper is one in a series that investigates topological measures on locally compact spaces. A measure defined open and closed sets; it finitely additive the collection of sets, inner regular outer sets. We examine semisolid sets give way constructing from solid-set functions compact, Hausdorff, connected, connected For spaces we present two simpler methods than currently available one. examples finite infinite an easy to generate whose one-point compactification has genus 0. Our results are necessary for various measures, additional properties provide tool determining whether or quasi-linear functionals same.