Sober topological spaces valued in a quantale
arXiv:2103.02801
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.
22 pages. arXiv admin note: text overlap with arXiv:2102.02939