A Novel Proof of the Heine-Borel Theorem

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dc.creatorMacauley, Matthew
dc.creatorRabern, Brian
dc.creatorRabern, Landon
dc.date2008-08-06
dc.date.accessioned2026-07-07T10:02:09Z
dc.date.available2026-07-07T10:02:09Z
dc.descriptionEvery 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.
dc.identifierhttps://arxiv.org/abs/0808.0844
dc.identifierhttp://arxiv.org/abs/0808.0844
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168873
dc.subjectHistory and Overview
dc.subjectLogic
dc.subjectMetric Geometry
dc.subject54E45; 03C99; 03F03
dc.titleA Novel Proof of the Heine-Borel Theorem
dc.typetext

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