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A Primer on Hilbert Space TheoryMetric Spaces

A Primer on Hilbert Space Theory: Metric Spaces [This chapter is concerned with the basic concepts of metric spaces and results that are most relevant to applications in Hilbert space theory. Assuming no prior knowledge of metric spaces, the definitions are given in detail and the relation to normed spaces made explicit early on. The main theorems proved are the Banach Fixed-Point Theorem, Baire’s Theorem, the equivalence between compact sets and complete totally bounded sets, and an account of completion.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Primer on Hilbert Space TheoryMetric Spaces

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Publisher
Springer International Publishing
Copyright
© Springer International Publishing Switzerland 2015
ISBN
978-3-319-03712-7
Pages
113 –147
DOI
10.1007/978-3-319-03713-4_4
Publisher site
See Chapter on Publisher Site

Abstract

[This chapter is concerned with the basic concepts of metric spaces and results that are most relevant to applications in Hilbert space theory. Assuming no prior knowledge of metric spaces, the definitions are given in detail and the relation to normed spaces made explicit early on. The main theorems proved are the Banach Fixed-Point Theorem, Baire’s Theorem, the equivalence between compact sets and complete totally bounded sets, and an account of completion.]

Published: Oct 9, 2014

Keywords: Metric space; Uniformly continuous function; Isometry; Banach fixed-point Theorem; Baire’s Theorem; Cauchy condition; Metric completion; Totally bounded space; Metric topology; Compact metric space

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