An elementary approach to exponentiable maps (Q1771114)

This study of elementary approach to exponentiable maps generalizes the first characterization of exponentiable spaces that are core-compact spaces. The paper reproves that exponentiable maps are necessarily fibrewise quasi locally compact. Using canonically topologized fibrewise function spaces, conversely it is proved that fibrewise quasi locally compact maps turn out to be exponentiable. The paper reproves and generalizes many known results in the category of topological spaces and continuous functions. It is moderately general in nature and may be pertinent to many cases of interests.