Abstract
The basic concept behind the subject of point-set topology is the notion of “closeness” between two points in a set X. In order to get a numerical gauge of how close together two points in X may be, we shall provide an extra structure to X, viz., a topological structure, that again goes beyond its purely settheoretic structure. For most of our purposes the notion of closeness associated with a metric will be sufficient, and this leads to the concept of “metric space”: a set upon which a “metric” is defined. The metric-space structure that a set acquires when a metric is defined on it is a special kind of topological structure. Metric spaces comprise the kernel of this chapter, but general topological spaces are also introduced.
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© 2011 Springer Science+Business Media, LLC
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Kubrusly, C.S. (2011). Topological Structures. In: The Elements of Operator Theory. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4998-2_3
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DOI: https://doi.org/10.1007/978-0-8176-4998-2_3
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Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4997-5
Online ISBN: 978-0-8176-4998-2
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