Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Power structures of directed spaces   Powerdomains in domain theory plays an important role in modeling the
semantics of nondeterministic functional programming languages.\ In this
paper,\ we extend the notion of powerdomain to the category of directed
spaces,\ which is equivalent to the notion of the\ $T_0$\ monotone-determined
space\ \cite{EN2009}.\ We define the notion of upper,\ lower and convex
powerspace of a directed space by the way of free algebras.\ We show that the
upper,\ lower and convex powerspace over any directed space exist and give
their concrete structures.\ Generally,\ the upper,\ lower and convex
powerspaces of a directed spaces are different from the upper,\ lower and
convex powerdomains of a dcpos endowed with the Scott topology and the
observationally-induced upper and lower powerspaces introduced by Battenfeld
and Sch\"{o}der in 2015. Keywords: powerdomain,\ directed lower powerspace of
directed spaces,\ directed upper powerspace of directed spaces,\ directed
convex powerspace of directed spaces,\ observationally-induced lower
powerspace,\ observationally-induced lower powerspace

23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex