Abstract
In this chapter we could ask either “Which functions are continuous?” or “What are the properties of continuous functions?“ The first question rests on limits, so we will defer it until after Chapter 5 and concentrate on properties of functions continuous on a closed interval.1 From past experience, or faith, or a peek at Chapter 7, we trust you are confident that there are such functions (e.g., polynomials).
We will use here the special definition of continuity on a closed interval discussed in Exercises 2.22 and following.
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© 2000 Springer-Verlag New York, Inc.
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(2000). Theorems about Continuous functions. In: Inside Calculus. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-22646-0_4
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DOI: https://doi.org/10.1007/978-0-387-22646-0_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98932-7
Online ISBN: 978-0-387-22646-0
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