ON GENERALIZED PRE-CLOSURE SPACES AND SEPARATION FOR SOME SPECIAL TYPES OF FUNCTIONS

In this paper, we show that a pointwise symmetric pre -isotonic pre -closure functions is uniquely determined by the pairs of sets it separates. We then show that when the pre -closure function of the domain is pre -isotonic and the pre -closure function of the codomain is pre -isotonic and pointwise-pre-symmetric, functions which separate only those pairs of sets which are already separated are pre -continuous.