Abstract
Every continuous function [a,b] →ℝ is uniformly continuous. There are three natural proofs of this theorem, using (a) The Nested Interval Theorem, (b) the Heine-Borel Theorem, and (c) the Bolzano-Weierstrass Theorem respectively.
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© 1982 Springer-Verlag New York, Inc.
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Moise, E.E. (1982). Necessary and Sufficient Conditions for Integrability. In: Introductory Problem Courses in Analysis and Topology. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8183-9_7
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DOI: https://doi.org/10.1007/978-1-4613-8183-9_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90701-7
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