Convergence near a point and the Arzela-Ascoli-type theorems

  • V. I. Kuzmich

Abstract

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.
Published
25.08.1993
How to Cite
KuzmichV. I. “Convergence Near a Point and the Arzela-Ascoli-Type Theorems”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 45, no. 8, Aug. 1993, pp. 1090–1095, https://umj.imath.kiev.ua/index.php/umj/article/view/5904.
Section
Research articles