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Continuity

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Book cover Elementary Analysis

Part of the book series: Undergraduate Texts in Mathematics ((UTM))

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Abstract

Most of the calculus involves the study of continuous functions. In this chapter we study continuous and uniformly continuous functions.

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Notes

  1. 1.

    One of the fine properties of compactness is: If a set is compact in some set, then it is compact in all sets.

  2. 2.

    Readers familiar with relative topologies will recognize this as stating that E is a disjoint union of nonempty relatively-open subsets of E.

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Authors and Affiliations

  1. Department of Mathematics, University of Oregon, Eugene, OR, USA

    Kenneth A. Ross

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  1. Kenneth A. Ross
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Ross, K.A. (2013). Continuity. In: Elementary Analysis. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6271-2_3

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