Abstract
In this chapter you will study the concept of connectedness. Roughly speaking, the idea is to distinguish those spaces and sets that split up into several pieces from those that are all one piece. This can be done in several different ways and I will take up just one such criterion. After the general ideas have been worked out, you will look at the situation on the real line and prove an important theorem — the Intermediate Value Theorem.
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© 1982 Springer-Verlag New York, Inc.
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Reisel, R.B. (1982). Connectedness. In: Elementary Theory of Metric Spaces. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8188-4_6
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DOI: https://doi.org/10.1007/978-1-4613-8188-4_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90706-2
Online ISBN: 978-1-4613-8188-4
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