The Arzelà-Ascoli theorem by means of ideal convergence
type: Item
instance of: scholarly article
title: The Arzelà-Ascoli theorem by means of ideal convergence
zbMATH Open document ID: 1404.40002
author: Emre Taş
author: T. Yurdakadim
published in: Georgian Mathematical Journal
publication date: 2018-10-10T00:00:00Z
review text: 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.
reviewed by: Sefa Anıl Sezer
Mathematics Subject Classification ID: 40A30
Mathematics Subject Classification ID: 40A35
zbMATH DE Number: 6950215
zbMATH Keywords: pointwise and uniform convergence
zbMATH Keywords: ideal convergence
zbMATH Keywords: Arzelà-Ascoli theorem
MaRDI profile type: Publication
full work available at URL: gmj-2017-0052
OpenAlex ID: W2772162400
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DOI: 10.1515/GMJ-2017-0052
description: scientific article; zbMATH DE number 6950215