‎In this paper‎, ‎we are interested in studying subgroups of topologized fundamental groups and their influences on generalized covering maps‎. ‎More precisely‎, ‎we find some relationships between generalized covering subgroups and the other famous subgroups of the fundamental group equipped with the compact-open topology and the whisker topology‎. ‎Moreover‎, ‎we present some conditions unde...

We show that the Scott topology induces a topology for real-valued Lipschitz maps on Banach spaces which we call the L-topology. It is the weakest topology with respect to which the L-derivative operator, as a second order functional on the space of Lipschitz maps into the domain of non-empty, convex and weak*-compact valued functions ordered by reverse inclusion, is continuous. For finite dime...

We discuss the domain-theoretic and topological content of the operator calculus used in the Irish School of the Vienna Development Method (VDM♣) of formal systems development. Thus, we examine the Scott continuity, or otherwise, of the basic operators used in this calculus when viewed as operators on the domain (X → Y ) of partial functions mapping X into Y . It turns out that the override, on...

We construct a complete lattice Z such that the binary supremum function sup : Z × Z → Z is discontinuous with respect to the product topology on Z × Z of the Scott topologies on each copy of Z. In addition, we show that bounded completeness of a complete lattice Z is in general not inherited by the dcpo C(X,Z) of continuous functions from X to Z where X may be any topological space and where o...

In this paper we show that a variation of a technique of Mǐskin and Tall yields a cocompact completely regular Moore space that is Scott-domain-representable and has a closed Gδ-subspace that is not Scott-domain-representable. This clarifies the general topology of Scott-domain-representable spaces and raises additional questions about Scott-domain representability in Moore spaces. 2000 AMS Cla...

in this paper, the urysohn and completely hausdorff axioms in general topology are generalized to l-topological spaces so as to be compatible with pointwise metrics. some properties and characterizations are also derived

We show that the Kantorovich-Rubinstein quasi-metrics dKR and dKRa of Part I extend naturally to various spaces previsions, in particular not just linear previsions (roughly, measures) I. There are natural isomorphisms between Hoare Smyth powerdomains, as used denotational semantics, discrete sublinear normalized superlinear respectively. Turning corresponding hyperspaces, namely same but equip...

Abstract Working constructively, we study continuous directed complete posets (dcpos) and the Scott topology. Our two primary novelties are a notion of intrinsic apartness sharp elements. Being apart is positive formulation being unequal, similar to how inhabitedness nonemptiness. To exemplify sharpness, note that lower real if only it located. first main result for large class dcpos, Bridges–V...

The purpose of this paper is to construct a weak hyper semi-quantale as a generalization of the concept of semi-quantale and used it as an appropriate hyperlattice-theoretic basis to formulate new lattice-valued topological theories. Based on such weak hyper semi-quantale, we aim to construct the notion of a weak hypervalued-topology as a generalized form of the so-called lattice-valued t...

Given a mapping $f:Xto X$ we naturally associate to it a monotonic map $gg_f:exp Xto exp X$ from the power set of $X$ into itself, thus inducing a generalized topology on $X$. In this paper we investigate some properties of generalized topologies which are defined by such a procedure.