Summary: We introduce the notions of pro-\(\theta\)-derived, pre-\(\theta\)-border, pre-\(\theta\)-frontier and pre-\(\theta\)-exterior of a set and study some of their basic properties. We also introduce two classes of functions called \(\theta\)-preopen functions and \(\theta\)-precloscd functions. We obtain their characterizations, their basic properties and their relationships with other types of functions between topological spaces.