Topological Structures

Carlos S. Kubrusly ()
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Carlos S. Kubrusly: Catholic University of Rio de Janeiro, Electrical Engineering Department

Chapter 3 in The Elements of Operator Theory, 2011, pp 87-198 from Springer

Abstract: 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.

Keywords: Open Subset; Topological Space; Topological Structure; Triangle Inequality; Open Ball (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-0-8176-4998-2_3

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