21 citations · 69 across the 17 of their papers we have counts for
17 papers
Formal balls of -categories
Xianbo Yang, Dexue Zhang
The construction of the formal ball model for metric spaces due to Edalat and Heckmann was generalized to -categories by Kostanek and Waszkiewicz. This paper concerns the…
The double contravariant powerset monad in the Goguen category of fuzzy sets
Sijia Lu, Dexue Zhang
A monad is constructed in the Goguen category of fuzzy sets valued in a unital quantale, which is an analog of the double contravariant powerset monad in the category of sets. With…
A Hofmann-Mislove theorem for approach spaces
Junche Yu, Dexue Zhang
The Hofmann-Mislove theorem says that the ordered set of open filters of the open-set lattice of a sober topological space is isomorphic to the ordered set of compact saturated set…
Sober topological spaces valued in a quantale
Dexue Zhang, Gao Zhang
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…
Continuous [0,1]-lattices and injective [0,1]-approach spaces
Junche Yu, Dexue Zhang
In 1972, Dana Scott proved a fundamental result on the connection between order and topology which says that injective spaces are precisely continuous lattices endowed with S…
The saturated prefilter monad
Hongliang Lai, Dexue Zhang, Gao Zhang
This paper considers some extensions of the notion of filter to the quantale-valued context, including saturated prefilter, -filter and bounded saturated prefilter. The quest…