Abstract
By pursuing the theme of building new classes of functions, we are led to some general considerations about continuity in this chapter. One outcome of this approach is a sketch of one way (there are several) of providing rigorous definitions of the so-called elementary functions and establishing their familiar properties. Perhaps the more important outcome is the appearance of certain fundamental concepts and theorems of Analysis and some clarification of exactly what variety of functions possess the property of continuity.
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© 1994 Springer Science+Business Media New York
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Pedrick, G. (1994). Continuous Functions. In: A First Course in Analysis. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8554-5_4
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DOI: https://doi.org/10.1007/978-1-4419-8554-5_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6435-4
Online ISBN: 978-1-4419-8554-5
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