Abstract
Metric spaces are introduced and many examples given of these structures. The core properties of completeness, compactness, connectedness and simple connectedness are examined; compactness and connectedness are motivated in a variety of ways. Special attention is paid to various forms of homotopy, and a natural link between simple connectedness and the fundamental group is established. Applications to differential equations are given.
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© 2014 Springer International Publishing Switzerland
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Dyer, R.H., Edmunds, D.E. (2014). Metric Spaces. In: From Real to Complex Analysis. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-06209-9_2
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DOI: https://doi.org/10.1007/978-3-319-06209-9_2
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-06208-2
Online ISBN: 978-3-319-06209-9
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