Equi-Baire one family of functions on metric spaces: A generalization of equi-continuity; and some applications

In this article we introduce a generalization of the concept of equicontinuity, namely the concept of Equi-Baire one for a family of functions on metric spaces. We use this concept to obtain some results similar to those existing in the literature that are derived from equicontinuity. We also give some applications, and investigate the relations between equi-Baire one property of the family F={fⁿ}_n=1 ^∞ for a Baire one function f and its dynamics.