For eagles only: probably the most difficult proof of the Arzelà-Ascoli theorem – via the Stone-Čech compactification

DOI10.2989/16073606.2017.1339741zbMath1422.54030OpenAlexW2729258845MaRDI QIDQ5236125

Marek Wójtowicz

Publication date: 15 October 2019

Published in: Quaestiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2989/16073606.2017.1339741

zbMATH Keywords

Stone-Čech compactificationArzelà-Ascoli theorem

Mathematics Subject Classification ID

Compactness (54D30) Banach spaces of continuous, differentiable or analytic functions (46E15) Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science (46B85)

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Metric compactness criteria involving sequences of mappings and a proof of the Ascoli-Arzelà theorem with the use of Bernstein polynomials

Cites Work

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• The Kolmogorov-Riesz compactness theorem
• A functional analysis point of view on the Arzela-Ascoli theorem
• The Ascoli-Arzela Theorem via Tychonoff's Theorem