Summary
In this chapter, we have examined the concept of completeness and have shown how to complete any metric space. We have demonstrated the completeness of some important spaces. We have shown that completeness of the Hausdorff metric depends only on completeness of the original metric. We have also proved two theorems, Baire’s and Banach’s, that have far-reaching consequences both for analysis and for problem solving in many other areas of application.
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© 2007 Springer-Verlag London Limited
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(2007). Completeness. In: Metric Spaces. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-84628-627-8_10
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DOI: https://doi.org/10.1007/978-1-84628-627-8_10
Publisher Name: Springer, London
Print ISBN: 978-1-84628-369-7
Online ISBN: 978-1-84628-627-8
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