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Chapter 4: Complete Normed Spaces

Chapter 4: Complete Normed Spaces

pp. 53-65

Authors

, University of Warwick
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Summary

We introduce the property of completeness and prove some abstract results about complete normed spaces (Banach spaces). We then give a number of examples of Banach spaces: l^p, L^p, and spaces of continuous functions. We then discuss convergence of series in Banach spaces and end the chapter with a proof of the Contraction Mapping Theorem.

Keywords

  • completeness
  • Banach spaces
  • sequence spaces
  • continuous functions
  • Contraction Mapping Theorem

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