The Arzelà-Ascoli theorem by means of ideal convergence
The concept of ideal convergence was introduced first by \textit{P. Kostyrko} et al. [Real Anal. Exch. 26, No. 2, 669--685 (2001; Zbl 1021.40001)]. Ideal convergence is a generalization of ordinary convergence and statistical convergence and it is based on an ideal of subsets of the set of positive integers. As a main result of this paper, the authors prove an ideal convergence version of the Arzelà-Ascoli theorem. Also, they describe the relation between equicontinuity and continuity by means of ideal convergence.
scientific article; zbMATH DE number 6950215
scientific article