Summary
In this chapter, we have examined the concept of boundedness for subsets of a metric space and the stronger concept of total boundedness. We have introduced bounded functions. We have also developed the Hausdorff metric for measuring distances between non-empty closed bounded subsets of any metric space, and we have presented a solution to the nearest-point problem.
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© 2007 Springer-Verlag London Limited
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(2007). Bounds. In: Metric Spaces. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-84628-627-8_7
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DOI: https://doi.org/10.1007/978-1-84628-627-8_7
Publisher Name: Springer, London
Print ISBN: 978-1-84628-369-7
Online ISBN: 978-1-84628-627-8
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