A Novel Proof of the Heine-Borel Theorem

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Every beginning real analysis student learns the classic Heine-Borel theorem, that the interval [0,1] is compact. In this article, we present a proof of this result that doesn't involve the standard techniques such as constructing a sequence and appealing to the completeness of the reals. We put a metric on the space of infinite binary sequences and prove that compactness of this space follows from a simple combinatorial lemma. The Heine-Borel theorem is an immediate corollary.

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History and Overview, Logic, Metric Geometry, 54E45; 03C99; 03F03

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http://salesiana.dossiersoluciones.com/handle/123456789/168873

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0808.0844
 http://arxiv.org/abs/0808.0844

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arXiv