相关论文: An Alternative Definition of the Completion of Met…

Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…

A round metric space is the one in which closure of each open ball is the corresponding closed ball. By a sleek metric space, we mean a metric space in which interior of each closed ball is the corresponding open ball. In this, article we…

Computable analysis and effective descriptive set theory are both concerned with complete metric spaces, functions between them and subsets thereof in an effective setting. The precise relationship of the various definitions used in the two…

Magnitude is a numerical isometric invariant of metric spaces, whose definition arises from a precise analogy between categories and metric spaces. Despite this exotic provenance, magnitude turns out to encode many invariants from integral…

In this paper we introduce the concept of the rectangular metric like spaces, along with its topology and we prove some fixed point theorems under different contraction principles. We introduce the concept of modified metric-like space as…

The aim of this paper is to discus the relations between various notions of sequential completeness and the corresponding notions of completeness by nets or by filters in the setting of quasi-metric spaces. We propose a new definition of…

The main purpose of this paper is to study complex valued metric-like spaces as an extension of metric-like spaces, complex valued partial metric spaces, partial metric spaces, complex valued metric spaces and metric spaces. In this…

We define a class of trim metric spaces and show that every finite metric space is the leaf space of a metric forest with trim base.

Magnitude is a real-valued invariant of metric spaces, analogous to the Euler characteristic of topological spaces and the cardinality of sets. The definition of magnitude is a special case of a general categorical definition that clarifies…

We observe that the category of topological space, uniform spaces, and simplicial sets are all, in a natural way, full subcategories of the same larger category, namely the simplicial category of filters; this is, moreover, implicit in the…

We give sufficient conditions for a finite metric space to be determined by the magnitude function. In particular, a generic finite metric space such that the distances between the points are rationally independent is determined by the…

In this paper we examine two basic topological properties of partial metric spaces, namely compactness and completeness. Our main result claims that in these spaces compactness is equivalent to sequential compactness. We also show that…

Measures play an important role in the characterisation of various function spaces. In this paper, the structure of density measures will be investigated. These are elements of the dual of the space of essentially bounded func- tions. The…

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…

We introduce the notion of tiling spaces for metric spaces. The class of tiling spaces contains the Euclidean spaces, the middle-third Cantor set, and various self-similar spaces appearing in fractal geometry. For doubling tiling spaces, we…

Metric spaces are generalized by many scholars. Recently, Khatami and Mirzavaziri use a mapping called $t$-definer to popularize the triangle inequality and give a generalization of the notion of a metric, which is called a $\star$-metric.…

A metric space is said to be all-set-homogeneous if any of its partial isometries can be extended to a genuine isometry. We give a classification of a certain subclass of all-set-homogeneous length spaces.

Magnitude is a numerical invariant of metric spaces introduced by Leinster, motivated by considerations from category theory. This paper extends the original definition for finite spaces to compact spaces, in an equivalent but more natural…

The main purpose of this paper is to find the fixed point in such cases where existing literature remain silent. In this paper we introduce partial completeness, a new type of contraction and many other definitions. Using this approach the…

We set up a model for reasoning about metric spaces with belief theoretic measures. The uncertainty in these spaces stems from both probability and metric. To represent both aspect of uncertainty, we choose an expected distance function as…