2021/03/04 by Zhang, Dexue, Zhang, Gao · 1 citation
#54A40 54B30 18B30 #Category Theory (math.CT) #FOS: Mathematics #General Topology (math.GN)
paper · doi:10.48550/arxiv.2103.02801
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.