Related papers: Strongly Continuous Domains
In this paper, we tailor-make new approximation operators inspired by rough set theory and specially suited for domain theory. Our approximation operators offer a fresh perspective to existing concepts and results in domain theory, but also…
Recently, J. D. Lawson encouraged the domain theory community to consider the scientific program of developing domain theory in the wider context of $T_0$-spaces instead of restricting to posets. In this paper, we respond to this calling by…
The study of weak domains and quasicontinuous domains leads to the consideration of two types generalizations of domains. In the current paper, we define the weak way-below relation between two nonempty subsets of a poset and quasiexact…
Two groups of naturally arising questions in the mathematical theory of domains for denotational semantics are addressed. Domains are equipped with Scott topology and represent data types. Scott continuous functions represent computable…
Recently, J. D. Lawson encouraged the domain theory community to consider the scientific program of developing domain theory in the wider context of $T_0$ spaces instead of restricting to posets. In this paper, we respond to this calling…
This article introduces strongly proximal continuous (s.p.c.) functions, strong proximal equivalence (s.p.e.) and strong connectedness. A main result is that if topological spaces $X,Y$ are endowed with compatible strong proximities and…
In functional analysis it is well known that every linear functional defined on the dual of a locally convex vector space which is continuous for the weak topology is the evaluation at a uniquely determined point of the given vector space.…
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…
Working constructively, we study continuous directed complete posets (dcpos) and the Scott topology. Our two primary novelties are a notion of intrinsic apartness and a notion of sharp elements. Being apart is a positive formulation of…
We present old and new characterizations of core spaces, alias worldwide web spaces, originally defined by the existence of supercompact neighborhood bases. The patch spaces of core spaces, obtained by joining the original topology with a…
The probabilistic powerdomain $\mathbf V X$ on a space $X$ is the space of all continuous valuations on $X$. We show that, for every quasi-continuous domain $X$, $\mathbf V X$ is again a quasi-continuous domain, and that the Scott and weak…
Working constructively, we study continuous directed complete posets (dcpos) and the Scott topology. Our two primary novelties are a notion of intrinsic apartness and a notion of sharp elements. Being apart is a positive formulation of…
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.…
Web spaces, wide web spaces and worldwide web spaces (alias C-spaces) provide useful generalizations of continuous domains. We present new characterizations of such spaces and their patch spaces, obtained by joining the original topology…
A non-empty subset of a topological space is irreducible if whenever it is covered by the union of two closed sets, then already it is covered by one of them. Irreducible sets occur in proliferation: (1) every singleton set is irreducible,…
We study properties of strongly separately continuous mappings defined on subsets of products of topological spaces equipped with the topology of pointwise convergence. In particular, we give a necessary and sufficient condition for a…
We will describe a new superconductivity mechanism, proposed by the authors in [1], which is based on a topologically ordered ground state rather than on the usual Landau mechanism of spontaneous symmetry breaking. Contrary to anyon…
In this paper, we give a topological version of Scott convergence theorem for locally hypercompact spaces. We introduce the notion of $\mathcal{S}^*_X$-convergence on a $T_0$ topological space $X$, and define the notion of finitely…
We introduce a continuous domain for function spaces over topological spaces which are not core-compact. Notable examples of such topological spaces include the real line with the upper limit topology, which is used in solution of initial…
The current work is motivated by the papers $[B_3]$, $[B_6]$, $[Be]$, $[Be-Tu]$. In particular, using Theorem 3.7 of $[B_3]$ and methods developed in this paper, the spectral and strong homology groups of continuous maps were defined and…