On the category of ordered pre-topological spaces

Abstract

A pre-topological space equipped with an order is called an ordered pre- topological space. These spaces form the objects of a category which will be de- noted by OVPT. The arrows of this category are certain increasing maps called V -continuous. Essentially, we will prove that the subcategory of ordered pre- topological spaces of type T0, OVPT0, is reflective in OVPT. We introduce and study some new separation axioms and characterize the class of morphisms orthog- onal to the objects of OVPT0.