On metric-preserving functions

Abstract

A function f:[0,infinity)->[0,infinity) is said to be metric-preserving if for every metric space (X,d), fod is a metric on X and a metric-preserving function f is said to be strongly metric-preserving if fod is topologically equivalent to d. In our investigation, we study some important properties of metric-preserving functions and strongly metric-preserving functions, especially those concerning completeness and totally boundedness