Characterizations of Pairwise Contra Pre-continuous

The aim of this paper is to study the notion of contra pre-continuous functions in a bitopological space called pairwise contra pre- continuous up on some generalizations of closed sets, namely pairwise pre-closed and pairwise pre-open sets. Also, we introduce pairwise contra pre-closed graphs and study some of their properties. In addition, we study the implications of these types of functions on some covering properties.