arXiv subjects

Longchun Wang

Publications and source records attributed to Longchun Wang.

3 recordsLinked to original sources

arXiv2021

D-completion, well-filterification and sobrification

In this paper, we obtain some sufficient conditions for the D-completion of a T0 space to be the well-filterification of this space, the well-filterification of a T0 space to be the sobrification of this space and the D-completion of a T0 space to be the sobrification, respectively. Moreover, we give an example to show that a tapered closed set may be neither the closure of a directed set nor the closed KF-set, respectively. Because the tapered closed set is a closed WD-set, the example also gives a negative answer to a problem proposed by Xu. Meantime, a new direct characterization of the D-completion of a T0 space is given by using the notion of pre-c-compact elements.

math.GN↗

arXiv2020

The categorical equivalence between disjunctive sequent calculi and algebraic L-domains

This paper establishes a purely syntactic representation for the category of algebraic L-domains with Scott-continuous functions as morphisms. The central tool used here is the notion of logical states, which builds a bridge between disjunctive sequent calculi and algebraic L-domains. To capture Scott-continuous functions between algebraic L-domains, the notion of consequence relations between disjunctive sequent calculi is also introduced. It is shown that the category of disjunctive sequent calculi with consequence relations as morphisms is categorical equivalent to that of algebraic L-domains with Scott-continuous functions as morphisms.

cs.LO↗

arXiv2018

Categorical Representations of Continuous Domains and Continuous L-Domains Based on Closure Spaces

Closure space has proven to be a useful tool to restructure lattices and various order structures.This paper aims to provide a novel approach to characterizing some important kinds of continuous domains by means of closure spaces. By introducing an additional map into a given closure space, the notion of F-augmented generalized closure space is presented. It is shown that F-augmented generalized closure spaces generate exactly continuous domains. Moreover, the notion of approximable mapping is identified to represent Scott-continuous functions between continuous domains. These results produce a category equivalent to that of continuous domains with Scottcontinuous functions. At the same time, two subclasses of F-augmented generalized closure spaces are considered which are representations of continuous L-domains and continuous bounded complete domains, respectively.

cs.LO↗