Topological Structures

  • Carlos S. Kubrusly


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.


Open Subset Topological Space Topological Structure Triangle Inequality Open Ball 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Electrical Engineering DepartmentCatholic University of Rio de JaneiroRio de JaneiroBrazil

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