Continuity

Steen Pedersen ()
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Steen Pedersen: Wright State University, Department of Mathematics

Chapter 5 in From Calculus to Analysis, 2015, pp 77-89 from Springer

Abstract: 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.

Keywords: Nested Interval Theorem; Extreme Value Theorem; Uniform Continuity; Compact Interval; Continuous Image (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-13641-7_5

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DOI: 10.1007/978-3-319-13641-7_5

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