English

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.

Keywords

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

R2 v1 2026-06-23T23:44:17.947Z