On the metric representations of affinely connected spaces

On the Structure of Metric-like Spaces

The main purpose of this paper is to introduce several concepts of the metric-like spaces. For instance, we define concepts such as equal-like points, cluster points and completely separate points. Furthermore, this paper is an attempt to present compatibility definitions for the distance between a point and a subset of a metric-like space and also for the distance between two subsets of a metr...

On Some Properties of Analytic Spaces Connected with Bergman Metric Ball

On planarity of compact, locally connected, metric spaces

Thomassen [Combinatorica 24 (2004), 699–718] proved that a 2–connected, compact, locally connected metric space is homeomorphic to a subset of the sphere if and only if it does not contain K5 or K3,3. The “thumbtack space” consisting of a disc plus an arc attaching just at the centre of the disc shows the assumption of 2–connectedness cannot be dropped. In this work, we introduce “generalized t...

On metric spaces induced by fuzzy metric spaces

For a class of fuzzy metric spaces (in the sense of George and Veeramani) with an H-type t-norm,  we present a method to construct a metric on a  fuzzy metric space. The induced metric space shares many important properties with the given fuzzy metric space.  Specifically, they generate the same topology, and have the same completeness. Our results can give the constructive proofs to some probl...

Concerning the Separability of Certain Locally Connected Metric Spaces

If a connected metric space S is locally separable, then S is separable. If a connected, locally connected, metric space S is locally peripherally separable, then S is separable. Furthermore if a connected, locally connected, complete metric space S satisfies certain "flatness" conditions, it is known to be separable. These "flatness" conditions are rather strong and involve both im kleinen and...