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Continuity

In: From Calculus to Analysis

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  • Steen Pedersen

    (Wright State University, Department of Mathematics)

Abstract

We discuss continuity and limit of monotone functions, the intermediate value theorem and show that a continuous image of a compact interval is a compact interval and that a continuous function defined on a compact interval is uniformly continuous. These results are all global in the sense that they depend on the function being continuous on an interval, the pointwise (local) results about continuity are contained in Chapter 2 . The main tool used in the proofs is the Nested Interval Theorem.

Suggested Citation

  • Steen Pedersen, 2015. "Continuity," Springer Books, in: From Calculus to Analysis, edition 127, chapter 5, pages 77-89, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-13641-7_5
    DOI: 10.1007/978-3-319-13641-7_5
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