– The aim of this paper is to introduce the concept of pre mX continuous function and to show some of its application. Also the concept of pre mX open mapping and pre mX homeomorphism is studied. The concept of pre mX open set has already been introduced by the authors in 2011.In this paper a topology is considered which is generated from mX structure and it is denoted as Tm. The concept of pre mX continuous X function is discussed in the topological space (X, Tm) generated from (X, mX). X