Сходимость возле точки и теоремы типа Арцела - Асколи - Кузьмич, В.И. (Український математичний журнал, 1993)
Theorems are proved giving necessary and sufficient conditions for the convergence of a sequence of continuous (differentiable) functions to a continuous (differentiable) function. The concepts of convergence near a point and equipotential convergence near a point are introduced. These concepts are introduced locally; on a segment, they are equivalent to the quasiuniform convergence and to the uniform convergence of a sequence of functions, respectively.