Sober topological spaces valued in a quantale
General Topology
2021-09-15 v2 Category Theory
Abstract
The notion of sobriety is extended to the realm of topological spaces valued in a commutative and unital quantale, via an adjunction between a category of quantale modules and the category of quantale-valued topological spaces. Relations between such sober spaces and quantale-valued domains based on flat ideals are investigated.
Cite
@article{arxiv.2103.02801,
title = {Sober topological spaces valued in a quantale},
author = {Dexue Zhang and Gao Zhang},
journal= {arXiv preprint arXiv:2103.02801},
year = {2021}
}
Comments
22 pages. arXiv admin note: text overlap with arXiv:2102.02939