This monograph, for the first time in book form, considers the large structure of metric spaces
as captured by bornologies: families of subsets that contain the singletons, that are stable …

In recent years Lipschitz-type functions have been studied in an extensive manner.
Particularly, we have locally Lipschitz functions (both the ball radius and the local Lipschitz …

In the context of real-valued functions defined on metric spaces, it is known that the locally
Lipschitz functions are uniformly dense in the continuous functions and that the Lipschitz in …

In this paper we introduce a realcompactification for any metric space (X, d), defined by
means of the family of all its real-valued uniformly continuous functions. We call it the …

A metric space (X, d) is called finitely chainable if for every ϵ> 0, there are finitely many
points p 1, p 2,..., pr in X and a positive integer m such that every point of X can be joined …

The main purpose of this paper is to explore normality in terms of distances between points
and sets. We prove some important consequences on realvalued contractions, ie functions …

The purpose of this article is to explore the very general phenomenon that a function
between metric spaces has a particular metric property if and only if whenever it is followed …

Abstract The classical Hahn-Banach theorem is based on a successive point-by-point
procedure of extending bounded linear functionals. In the setting of a general metric domain …

A function between two metric spaces is said to be Cauchy-regular if it takes Cauchy
sequences to Cauchy sequences. This well-studied class of functions lies strictly in between …

Metric spaces satisfying properties stronger than completeness and weaker than
compactness have been the subject of study for a number of articles over the years. Two …