Related papers: Scott approach distance on metric spaces
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$_0$…
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…
Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an…
The paper introduces the class of O-metric spaces, a novel generalization of metric-type spaces, classifying almost all possible metric types into upward and downward O-metrics. We list some topologies arising from O-metrics and discuss…
Metric spaces $(X, d)$ are ubiquitous objects in mathematics and computer science that allow for capturing (pairwise) distance relationships $d(x, y)$ between points $x, y \in X$. Because of this, it is natural to ask what useful…
In this paper, we introduce a novel distance-like notion of furtherness for finite topological spaces, demonstrating that every finite space can be viewed as an asymmetric pseudometric space. In particular, we show that every finite T0…
In this paper, a new structure is defined on a topological space that equips the space with a concept of distance in order to do that firstly, a generalization of quasi-pseudo-metric space named R.O-metric space is introduced, and some of…
Gromov introduced two distance functions, the box distance and the observable distance, on the space of isomorphism classes of metric measure spaces and developed the convergence theory of metric measure spaces. We investigate several…
The aim of this paper is to establish the equivalence between the concepts of an $S$-metric space and a cone $S$-metric space using\ some topological approaches. We introduce a new notion of $TVS$-cone $S$-metric space using some facts…
We develop various Ehrenfeucht-Fra\"{\i}ss\'{e} games for distances between metric structures. We study two forms of distances: pseudometrics stemming from mapping spaces onto each other with some form of approximate isomorphism, and…
In 1972, Dana Scott proved a fundamental result on the connection between order and topology which says that injective $T_0$ spaces are precisely continuous lattices endowed with Scott topology. This paper investigates whether this is true…
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…
Hodge theory is a beautiful synthesis of geometry, topology, and analysis, which has been developed in the setting of Riemannian manifolds. On the other hand, spaces of images, which are important in the mathematical foundations of vision…
A labeled metric space is intuitively speaking a metric space together with a special set of points to be understood as the geometric boundary of the space. We study basic properties of a recently introduced labeled Gromov-Hausdorff…
We investigate when the space $\mathcal O_X$ of open subsets of a topological space $X$ endowed with the Scott topology is core compact. Such conditions turn out to be related to infraconsonance of $X$, which in turn is characterized in…
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
A method of induction the distances with Hilbert structure is proposed. Some properties of the method are studied. Typical examples of corresponding metric spaces are discussed. Key words: Hilbert spaces; metric spaces; isometric embedding…
A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…
The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…
We study the usual notion of Scott rank but in the setting of Polish metric spaces. The signature consists of distance relations: for each rational $q > 0$, there is a relation $R_{<q}(x,y)$ stating that the distance of $x$ and $y $ is less…