Related papers: Scott approach distance on metric spaces
Concept of bi-soft topological spaces is introduced. Several notions of a soft topological space are generalized to study bi-soft topological spaces. Separation axioms play a vital role in study of topological spaces. These concepts have…
Given a metric pair $(X,A)$, i.e. a metric space $X$ and a distinguished closed set $A \subset X$, one may construct in a functorial way a pointed pseudometric space $\mathcal{D}_\infty(X,A)$ of persistence diagrams equipped with the…
The definition of weighted distance measure involves weights. The paper proposes a weighted distance measure without the help of weights. Here, weights are intrinsically added to the measure, and for this, the concept of metric space is…
We give a notion of Scott rank for separable metric structures based on the definability of the (metric closures of) automorphism orbits in continuous infinitary logic. This is a continuous analogue of work of Montalb\'an for countable…
Given an Euclidean space, this paper elucidates the topological link between the partial derivatives of the Minkowski functional associated to a set (assumed to be compact, convex, with a differentiable boundary and a non-empty interior)…
The study of topological information of spatial objects has for a long time been a focus of research in disciplines like computational geometry, spatial reasoning, cognitive science, and robotics. While the majority of these researches…
Any discrete approach to quantum gravity must provide some prescription as to how to deduce continuum properties from the discrete substructure. In the causal set approach it is straightforward to deduce timelike distances, but surprisingly…
The notion of a spectral geometry on a compact metric space X is introduced. This notion serves as a discrete approximation of X motivated by the notion of a spectral triple from non-commutative geometry. A set of axioms charaterising…
Distance metric learning can be viewed as one of the fundamental interests in pattern recognition and machine learning, which plays a pivotal role in the performance of many learning methods. One of the effective methods in learning such a…
The concept of homotopic distance and its higher analog are introduced in [6]. In this paper we introduce some important properties of higher homotopic distance, investigate the conditions under which $\cat$, $\secat$ and higher dimensional…
We propose a geometric interpretation for the Stokes phenomenon in de Sitter spacetime that particles are produced in even dimensions but not in odd dimensions. The scattering amplitude for a quantum field between the in-vacuum and the…
In analogy to a result due to Drake and Thron about topological spaces, this paper studies the dcpos (directed complete posets) which are fully determined, among all dcpos, by their lattices of all Scott-closed subsets (such dcpos will be…
In this project we explore the geometry of general metric spaces, where we do not necessarily have the tools of differential geometry on our side. Some metric spaces $(X,d)$ allow us to define geodesics, permitting us to compare geodesic…
In arXiv:1801.01238 a variation of Bowen's topological entropy that can be applied to the study of discontinuous semiflows on compact metric spaces was introduced. The main novetly is the use of certain family of pseudosemimetrics…
We investigate a tangent space at a point of a general metric space and metric space valued derivatives. The conditions under which two different subspace of a metric space have isometric tangent spaces in a common point of these subspaces…
In this paper,the concepts of generalized ideal inf-limit and generalized ideal final lower bound limit are introduced in the directed complete poset,and their relations with Scott topology and Lawson topology are studied. The main results…
This paper surveys the significant progress over the past couple of decades in the theory of stratified spaces through the application of controlled methods as well as through the application of intersection homology.
The unsteady motion of a gas-liquid interface, such as during splashing or atomization, often results in complex liquid structures embedded in the ambient fluid. Here we explore the use of skeletonization to identify the minimum amount of…
This paper studies the properties of a new lower bound for the natural pseudo-distance. The natural pseudo-distance is a dissimilarity measure between shapes, where a shape is viewed as a topological space endowed with a real-valued…
In the directed setting, the spaces of directed paths between fixed initial and terminal points are the defining feature for distinguishing different directed spaces. The simplest case is when the space of directed paths is homotopy…