The notion of rare continuity was introduced by Popa {15} as a new generalization of weak continuity {7}. In this paper, we introduce a new class of functions called rarely pre- θ -continuous functions as a new generalization of the class of strongly θ -precontinuous functions and investigate some of its fundamental properties.

Popa [13] introduced the notion of rare continuity. In the same spirit, we introduce a new class of functions called rarely βθ-continuous functions by utilizing the notion of β-θ-open sets. We also investigate some of its fundamental properties. This type of continuity is stronger that rare β-continuity [9]. / En este paper nosotros introducimos una nueva clase de función denominada función raramente βθ-continua usando la noción de conjuntos β-θ-abiertos. Este tipo de continuidad es una noción más fuerte que lanoción de función rare β-continua dada por Jafari [9].