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5 - Metric and Normed Spaces

from Part II - Elements Of Classical Functional Analysis

Published online by Cambridge University Press:  06 January 2022

Martin Buntinas
Martin Buntinas
Affiliation:
Loyola University, Chicago
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Summary

Metric Spaces, Normed Spaces, and Banach Spaces are investigated. Topological concepts of Open and Closed sets, Convergence, Continuity, Compactness, Completeness, and Total Boundedness are studied. The Stone–Weierstrass Approximation Theorem is proven.

Keywords

Metric SpacesNormed SpacesTopologySeminormBanach SpacesConvergenceContinuityCompactnessStone–Weierstrass ApproximationComplete Spaces
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Classical and Discrete Functional Analysis with Measure Theory , pp. 169 - 213
Publisher: Cambridge University Press
Print publication year: 2022

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  • Metric and Normed Spaces
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.009
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  • Metric and Normed Spaces
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.009
Available formats
×

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To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Metric and Normed Spaces
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.009
Available formats
×