Real Analysis Exchange

A Convergence-Theoretic Viewpoint on the Arzelá-Ascoli Theorem

Frédéric Mynard

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Abstract

This is an expository note, hopefully accessible to students, on how continuous convergence and convergence-theroretic techniques can provide insight on the classical Arzelá-Ascoli theorem.

Article information

Source
Real Anal. Exchange Volume 38, Number 2 (2012), 431-444.

Dates
First available in Project Euclid: 27 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.rae/1403894903

Mathematical Reviews number (MathSciNet)
MR3261888

Zentralblatt MATH identifier
1295.54004

Subjects
Primary: 54A20: Convergence in general topology (sequences, filters, limits, convergence spaces, etc.) 54C35: Function spaces [See also 46Exx, 58D15]
Secondary: 54D30: Compactness

Keywords
Arzela-Ascoli Theorem function space compactness convergence space filter continuous convergence

Citation

Mynard, Frédéric. A Convergence-Theoretic Viewpoint on the Arzelá-Ascoli Theorem. Real Anal. Exchange 38 (2012), no. 2, 431--444.https://projecteuclid.org/euclid.rae/1403894903


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