Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semisolid sets and topological measures   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.

25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg