Independent form of (θ, s)-continuous functions in topological spaces.

We introduce a new class of almost contra-P β -continuous functions which is a subclass of the class of almost contra-precontinuous functions [8]. This class contains the classes of regular set connected functions, perfectly continuous functions and contra-P β -continuous functions. It is shown that almost contra-P β -continuity is independent to (θ, s)-continuity [12] and contra-precontinuity [11]. Furthermore, we obtain basic properties and preservations theorems for almost contra-P β -continuity. [ABSTRACT FROM AUTHOR]