Pointwise Compatibility, Lattices of f‐proximities and Counterexamples
Pramila Srivastava, Mona Khare · Annals of the New York Academy of Sciences · 1994
ABSTRACT: The concept of pointwise compatibility in the family of all basic proximities on a set X is introduced and studied. It is proved that the family of all pointwise compatible f‐proximities, under suitable restrictions on f, forms a complete distributive lattice. To the known f‐proximities is added a new proximity, termed as p‐proximity. Counterexamples are constructed in answer to questions regarding the existing one‐way implications for different f‐proximities.