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 set-theoretic 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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media New York
About this chapter
Cite this chapter
Kubrusly, C.S. (2001). Topological Structures. In: Elements of Operator Theory. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-3328-0_3
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3328-0_3
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4757-3330-3
Online ISBN: 978-1-4757-3328-0
eBook Packages: Springer Book Archive