Related papers: Metric 1-spaces
This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.
Recently many papers on cone metric spaces have been appeared, and main topological properties of such spaces have been obtained. A cone metric space is Hausdorff, and first countable, so the topology of it coincides with a topology induced…
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 paper deals with pretangent spaces to general metric spaces. An ltrametricity criterion for pretangent spaces is found and it is closely related to the metric betweenness in the pretangent spaces.
In models of emergent gravity the metric arises as the expectation value of some collective field. Usually, many different collective fields with appropriate tensor properties are candidates for a metric. Which collective field describes…
We show a possibility to apply certain philosophical concepts to the analysis of concrete mathematical structures. Such application gives a clear justification of topological and geometric properties of considered mathematical objects.
Metric currents are, in a certain sense, a metric analogous of flat currents, therefore are related to the geometry of the space and of their support. In this short note, we try to give some evidence for the previous statement, by showing…
The fixed-point theory and its applications to various areas of science are well known. In this paper we present some existence and uniqueness theorems for fixed circles of self-mappings on metric spaces with geometric interpretation. We…
In this paper, we discuss recent results about generalized metric spaces and fixed point theory. We introduce the notion of $\eta$-cone metric spaces, give some topological properties and prove some fixed point theorems for contractive type…
The space of all Riemannian metrics is infinite-dimensional. Nevertheless a great deal of usual Riemannian geometry can be carried over. The superspace of all Riemannian metrics shall be endowed with a class of Riemannian metrics; their…
If $X$ is a (topological) space, the $n$th finite subset space of $X$, denoted by $X(n)$, consists of $n$-point subsets of $X$ (i.e., nonempty subsets of cardinality at most $n$) with the quotient topology induced by the unordering map…
A topological space $X$ is cometrizable if it admits a weaker metrizable topology such that each point $x\in X$ has a (not necessarily open) neighborhood base consisting of metrically closed sets. We study the relation of cometrizable…
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…
Let M be a complete metric space. It is proved that if the space or scalar-valued bounded continuous functions on M admits an isometric shift, then M is separable.
The paper constructs a generalized metrical multi-time Lagrange space, which allows a natural development of relativistic geometrical optics theories, in a general setting.
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…
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…
In this paper, we introduce a generalization of rectangular $b-$metric spaces, by changing the rectangular inequality as follows \begin{equation*} \rho(x,y)\le \theta(x,y,u,v)[\rho(x,u)+\rho(u,v)+\rho(v,y)], \end{equation*}% for all…
The metric dimension of a general metric space was defined in 1953, applied to the set of vertices of a graph metric in 1975, and developed further for metric spaces in 2013. It was then generalised in 2015 to the k-metric dimension of a…
Contemporary relativity theory is restricted in two points: (1) a use of the Riemannian space-time geometry and (2) a use of inadequate (nonrelativistic) concepts. Reasons of these restrictions are analysed in [1]. Eliminating these…