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.