Continuous Differentiability in the Context of Generalized Approach to Differentiability

Recently, in their paper, the authors generalized notion of differentiability by defining it for all points functional domain (not only interior points) which can be considered meaningful. In this continuous is introduced differentiable function f:X→Rm with a not necessarily open X⊆Rn; i.e., continuity mapping df:X→HomRn,Rm considered. addition to introducing context approach differentiability, its characterization also given. It proved that derivatives at some direction n linearly independent vectors implies (continuous) differentiability.