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 …

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 …

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 …

Let X and Y be metric spaces. A function f: X → Y f: X→ Y is said to be Lipschitz in the small if
there are r> 0 r> 0 and K< ∞ K<∞ so that d (f (u), f (v)) ≤ Kd (u, v) d (f (u), f (v))≤ K d (u, v) …

This article provides necessary and sufficient conditions on the structure of a metric space
such that for various vector lattices of real-valued Lipschitz-type functions defined on the …

In recent years, Lipschitz-type functions have been studied in an extensive manner.
Particularly, we have locally Lipschitz functions, uniformly locally Lipschitz functions and …

The class of cofinally complete metric spaces lies between the class of complete metric
spaces and that of compact metric spaces. It is known that a metric space (X, d) is cofinally …

A function f from a metric space (X, d) to another metric space (Y, ρ) is said to be Cauchy-
continuous if for every Cauchy sequence (xn) in (X, d),(f (xn)) is Cauchy in (Y, ρ). It is well …

In the context of functions between metric spaces, we introduce a class of functions that
simultaneously provides characteristic answers to the following two questions:(1) What …