Related papers: Core spaces, sector spaces and fan spaces: a topol…
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…
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…
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…
In this paper, we unify various approaches to generalized covering space theory by introducing a categorical framework in which coverings are defined purely in terms of unique lifting properties. For each category $\mathcal{C}$ of…
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…
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…
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…
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…
We give geometric characterisations of patch and Lawson topologies in the context of predicative point-free topology using the constructive notion of located subset. We present the patch topology of a stably locally compact formal topology…
We explore a new connection between synthetic domain theory and Grothendieck topoi related to the distributive lattice classifier. In particular, all the axioms of synthetic domain theory (including the inductive fixed point object and the…
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…
Two closely related classes of topological spaces are fences and fans. A fence is a compact metric space whose components are either arcs or singletons. A fan is a continuum formed by joining arcs at a common vertex, in such a way that…
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.…
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…
The category of monotone determined spaces is an extended topological framework for dcpos in domain theory. We first show that monotone determined spaces are exactly the spaces generated by one-point convergence spaces, and then naturally…
In analogy to the situation for continuous lattices which were introduced by Dana Scott as precisely the injective T$_0$ spaces via the (nowadays called) Scott topology, we study those metric spaces which correspond to injective T$_0$…
A family of closed subsets of a topological space $X$ is called a (strict) $Cld$-fan in $X$ if this family is (strictly) compact-finite but not locally finite in $X$. Applications of (strict) $Cld$-fans are based on a simple observation…
Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law. Resting on this…
We investigated domain wall networks as a possible candidate to explain the present accelerated expansion of the universe. We discuss various requirements that any stable lattice of frustrated walls must obey and propose a class of `ideal'…
Locales have been studied as "topologies without points", mainly by tools of category theory. While traditional topology presents a space as a set of points with specified neighborhoods, localic topology presents a space as a lattice of…