ON θ-PROXIMITIES AND RELATED f-PROXIMITIES

Abstract

We show that every θ-proximity as defined by V.V. Fedorčuk is an f-proximity which we call a k-proximity. Two related f-proximities are introduced, viz. t- and d-proximities. The smallest and largest members of M_f(X, c) for f=k, d and t are characterised where M_f(X, c) is the family of f-proximities compatible with a given closure space (X, c).