相关论文: Representations of domains via closure spaces in t…
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…
With a frame $L$ as the truth value table, we study the topological representations for frame-valued domains. We introduce the notions of locally super-compact $L$-topological space and strong locally super-compact $L$-topological space.…
Representations of domains mean in a general way representing a domain as a suitable family endowed with set-inclusion order of some mathematical structures. In this paper, representations of domains via CF-approximation spaces are…
Directed spaces are natural topological extensions of dcpos in domain theory and form a cartesian closed category. We will show that the D-completion of free algebras over a Scott space $\Sigma L$, on the context of directed spaces, are…
Earlier an arbitrary poset $P$ was proved to be isomorphic to the collection of subsets of a space $M$ with two closures which are closed in the first closure and open in the other. As a space $M$ for this representation an algebraic dual…
In this paper, by means of upper approximation operators in rough set theory, we study representations for sL-domains and its special subclasses. We introduce the concepts of sL-approximation spaces, L-approximation spaces and…
We introduce constrained polynomial zonotopes, a novel non-convex set representation that is closed under linear map, Minkowski sum, Cartesian product, convex hull, intersection, union, and quadratic as well as higher-order maps. We show…
We develop the theory of continuous and algebraic domains in constructive and predicative univalent foundations, building upon our earlier work on basic domain theory in this setting. That we work predicatively means that we do not assume…
For a small quantaloid $\mathcal{Q}$, a $\mathcal{Q}$-closure space is a small category enriched in $\mathcal{Q}$ equipped with a closure operator on its presheaf category. We investigate $\mathcal{Q}$-closure spaces systematically with…
In this paper, concepts of (topological) FS-approximation spaces are introduced. Representations of FS-domains and BF-domains via (topological) FS-approximation spaces are considered. It is proved that the collection of CF-closed sets in an…
We characterize the real interpolation space between a weighted $L^p$ space and a weighted Sobolev space in arbitrary bounded domains in $\mathbb{R}^n$, with weights that are positive powers of the distance to the boundary.
We introduce continuous $R$-valuations on directed-complete posets (dcpos, for short), as a generalization of continuous valuations in domain theory, by extending values of continuous valuations from reals to so-called Abelian d-rags $R$.…
We propose a generalization of continuous lattices and domains through the concept of enriched closure space, defined as a closure space equipped with a preclosure operator satisfying some compatibility conditions. In this framework we are…
Faithful representations of regular $\ast$-rings and modular complemented lattices with involution within orthosymmetric sesquilinear spaces are studied within the framework of Universal Algebra. In particular, the correspondence between…
We give a commutative valuations monad Z on the category DCPO of dcpo's and Scott-continuous functions. Compared to the commutative valuations monads given in [Jia et al., 2021], our new monad Z is larger and it contains all push-forward…
We develop domain theory in constructive univalent foundations without Voevodsky's resizing axioms. In previous work in this direction, we constructed the Scott model of PCF and proved its computational adequacy, based on directed complete…
In this paper, the notion of dimension preserving approximation for real-valued bivariate continuous functions, defined on a rectangular domain $\rectangle$, has been introduced and several results, similar to well-known results of…
Formal Concept Analysis has proven to be an effective method of restructuring complete lattices and various algebraic domains. In this paper, the notions of attribute continuous formal context and continuous formal concept are introduced by…
Generalized intent discovery aims to extend a closed-set in-domain intent classifier to an open-world intent set including in-domain and out-of-domain intents. The key challenges lie in pseudo label disambiguation and representation…
We develop domain theory in constructive and predicative univalent foundations (also known as homotopy type theory). That we work predicatively means that we do not assume Voevodsky's propositional resizing axioms. Our work is constructive…