Abstract
The study of metric spaces preceded the study of topological spaces. The emerging awareness of the significance of the so-called open sets in metric spaces led to the concept of a topological space. Although many properties of topological spaces that have been studied extensively are motivated by our understanding of metric spaces, there are many topological spaces that are quite different from metric spaces. When we relax the conditions on a space so that we no longer have a metric we may get some surprising (and unpleasant) properties.
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© 1995 Springer-Verlag New York, Inc.
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Howes, N.R. (1995). Metric Spaces. In: Modern Analysis and Topology. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0833-4_1
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DOI: https://doi.org/10.1007/978-1-4612-0833-4_1
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97986-1
Online ISBN: 978-1-4612-0833-4
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