Abstract
In this chapter, we will define the fundamental notions of limits and continuity of functions and study the properties of continuous functions. We will discuss these properties in more general context of a metric space. The concept of compactness will be introduced. Next, we will focus on connectedness and investigate the relationships between continuity and connectedness. Finally, we will introduce concepts of monotone and inverse functions and prove a set of Intermediate Value Theorems.
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© 2007 Springer Science+Business Media, LLC
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(2007). Continuity. In: Principles of Mathematics in Operations Research. International Series in Operations Research & Management Science, vol 97. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-37735-3_11
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DOI: https://doi.org/10.1007/978-0-387-37735-3_11
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-37734-6
Online ISBN: 978-0-387-37735-3
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