Proximity Boolean algebra

Abstract

 The aim of this paper is to introduce the concept of proximity Boolean algebra.

We consider a complete Boolean algebra $B$ and define a proximity relation $\delta$ on $B$.

Some properties of the proximity Boolean algebra $(B,\delta)$ are given.

Also, we define the concept of proximity Boolean algebra map and introduce a new category,

which is called proximity Boolean algebra category and

obtain some basic results of this category, such as existence of product and equalizers.