Real Analysis Exchange

A Convergence-Theoretic Viewpoint on the Arzelá-Ascoli Theorem

Frédéric Mynard

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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

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

First available in Project Euclid: 27 June 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


Mynard, Frédéric. A Convergence-Theoretic Viewpoint on the Arzelá-Ascoli Theorem. Real Anal. Exchange 38 (2012), no. 2, 431--444.

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