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