A New Proof on Embedding the Category of Proximity Spaces into the Category of Nearness Spaces

Abstract

This paper establishes an explicit embedding functor from the category of the proximity spaces into the category of nearness spaces. This is done by defining methods to constructively inducing a proximity structure with a given nearness structure and vis versa. Those induction methods provide useful tools to understand the inter-relations and to translate the result between the two types of spaces.