Continuity of Powerspaces Structures in Directed Spaces
General Topology
2022-12-14 v2 Category Theory
Abstract
Powerspaces of directed spaces play an important role in modeling the semantics of nondeterministic functional programming languages. The notions of upper,lower and convex powerspace of a directed space are defined by the way of free algebras[25]. In this paper, We study the continuity of power structures of directed spaces and show that the directed lower powerspaces, directed upper powerspaces and directed convex powerspaces of continuous spaces are continuous spaces.
Cite
@article{arxiv.2211.08595,
title = {Continuity of Powerspaces Structures in Directed Spaces},
author = {Wu Wang},
journal= {arXiv preprint arXiv:2211.08595},
year = {2022}
}
Comments
the idea is studied by Hui kou