Convergence near a point and the Arzela-Ascoli-type theorems
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.
English version (Springer): Ukrainian Mathematical Journal 45 (1993), no. 8, pp 1215-1220.
Citation Example: Kuzmich V. I. Convergence near a point and the Arzela-Ascoli-type theorems // Ukr. Mat. Zh. - 1993. - 45, № 8. - pp. 1090–1095.