Some Aspects of Convergence via Pre-open Sets

In the literature of topological spaces, it is available that nearly compact spaces are equivalent to $po$-compact spaces. In the present note some characterizations concerning filters and nets are established on studying nearly compact spaces in the sense of $po$-compact spaces. The effects of pre-open sets on some particular types of functions, e.g., nearly continuous functions, $po$-graph via nets are also ascertained.