Abstract
In the theory of metric spaces, sequences play a fundamental role. Recall that a function from one metric space to another is continuous if it preserves convergent sequences (Proposition 1.12) and that a metric space is compact if each sequence has a convergent subsequence (Theorem 1.10). Furthermore, it is possible to characterize the topology in metric spaces by means of convergent sequences (e.g., Proposition 1.10 and Corollary 1.6).
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© 1995 Springer-Verlag New York, Inc.
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Howes, N.R. (1995). Transfinite Sequences. In: Modern Analysis and Topology. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0833-4_3
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DOI: https://doi.org/10.1007/978-1-4612-0833-4_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97986-1
Online ISBN: 978-1-4612-0833-4
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