Metric Spaces and Normed Linear Spaces

Avishek Adhikari () and Mahima Ranjan Adhikari ()
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Avishek Adhikari: Presidency University, Department of Mathematics
Mahima Ranjan Adhikari: Institute for Mathematics, Bioinformatics, Information Technology and Computer Science (IMBIC)

Chapter Chapter 2 in Basic Topology 1, 2022, pp 37-122 from Springer

Abstract: 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.

Date: 2022
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DOI: 10.1007/978-981-16-6509-7_2

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