New Type of Generalized Continuous Functions in Proximity Topological Space

Abstract

The paper deals with the importance of the continuum theory as a mathematical concept and its great role in solving many problems. Since the term proximity is a modern term, we were able in this research to answer a very important question: Is it possible to study types of continuity in proximity space like the types found in the usual topological space? In this research, we were able to find a type of continuity continuous) and obtain many results, relying on proximity theories and the different definitions of proximity space, and we were able to link them to the new definition that was established.