Proximal Relator Spaces

Abstract

This article introduces proximal relator spaces. The basic approach is to define a nonvoid family of proximity relations R-delta Phi (called a proximal relator) on a nonempty set. The pair (X,R-delta Phi) (also denoted X(R-delta Phi)) is called a proximal relator space. Then, for example, the traditional closure of a subset of the Sz'az relator space (X,R) can be compared with the more recent descriptive closure of a subset of (X,R-delta Phi). This leads to an extension of fat and dense subsets of the relator space (X,R) to proximal fat and dense subsets of the proximal relator space (X,R-delta Phi).