Metric Preserving Functions

Abstract

The primary topic of this paper is distance (or metric ) preserving functions. In particular, the paper will focus on the least integer function - a step function, also referred to as the ceiling function. Herein, the author will provide information about the ceiling function, as well as a proof that it is indeed metric preserving, supported by Wilson's Theorem and the Borsik-Dobos Theorem. In addition, the paper will show that the amenable condition and triangle triplet condition guarantee that a function is distance preserving.