Summary
After introducing open and closed balls, we showed that all open sets are unions of open balls and that boundary, closure and interior can be identified using open balls. We showed that balls in normed linear spaces are all convex and balanced and that, in any given space, they all have the same shape.
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© 2007 Springer-Verlag London Limited
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(2007). Balls. In: Metric Spaces. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-84628-627-8_5
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DOI: https://doi.org/10.1007/978-1-84628-627-8_5
Publisher Name: Springer, London
Print ISBN: 978-1-84628-369-7
Online ISBN: 978-1-84628-627-8
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