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Prerequisites: Sets, Algebraic Systems and Classical Analysis Read chapter Read first chapter

2022 | OriginalPaper | Chapter

2. Metric Spaces and Normed Linear Spaces

Authors : Avishek Adhikari, Mahima Ranjan Adhikari

Published in: Basic Topology 1

Publisher: Springer Nature Singapore

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Abstract

This chapter starts a journey in metric spaces describing the concept of metrics, which is an abstraction of distance in the Euclidean space and conveys an axiomatic framework for this abstraction with a systemic study of elementary basic properties of metric spaces. It also discusses normed linear spaces which form a versatile class of metric spaces. This discussion includes a brief study of Banach and Hilbert spaces.

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previous chapter Prerequisites: Sets, Algebraic Systems and Classical Analysis
next chapter Topological Spaces and Continuous Maps
Literature
  1. Adhikari, M.R.: Basic Algebraic Topolgy and Its Applications. Springer, India (2016)View Article
  2. Adhikari, M.R.: Basic Topology. Volume 3: Algebraic Topology and Topology of Fiber Bundles. Springer, India (2022)
  3. Adhikari, M.R., Adhikari, A.: Basic Modern Algebra with Applications. Springer, New Delhi, New York, Heidelberg (2014)View Article
  4. Adhikari, A., Adhikari, M.R.: Basic Topology. Volume 2: Topological Groups, Topology of Manifolds and Lie Groups. Springer, India (2022)
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Metadata
Title
Metric Spaces and Normed Linear Spaces
Authors
Avishek Adhikari
Mahima Ranjan Adhikari
Copyright Year
2022
Publisher
Springer Nature Singapore
Book
Basic Topology 1

Print ISBN: 978-981-16-6508-0

Electronic ISBN: 978-981-16-6509-7

Copyright Year: 2022

DOI
https://doi.org/10.1007/978-981-16-6509-7_2

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