Abstract
In this chapter we present the main definitions and results related to metric spaces. Standard topics such as open, closed, and compact sets are developed in detail. In the final section we prove the Heine–Borel theorem.
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References
W. Rudin, Principles of Mathematical Analysis (McGraw Hill, New York, 1976)
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Botelho, F.S. (2018). Metric Spaces. In: Real Analysis and Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-78631-5_2
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DOI: https://doi.org/10.1007/978-3-319-78631-5_2
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-78630-8
Online ISBN: 978-3-319-78631-5
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