Metric Spaces

Erscheinungsjahr 2008
ISBN: 978-0-521-35732-6
Verlag: Cambridge University Press

Buch, Englisch, Band 57, 152 Seiten, Format (B × H): 140 mm x 216 mm, Gewicht: 201 g

Reihe: Cambridge Tracts in Mathematics

Metric space topology, as the generalization to abstract spaces of the theory of sets of points on a line or in a plane, unifies many branches of classical analysis and is necessary introduction to functional analysis. Professor Copson's book, which is based on lectures given to third-year undergraduates at the University of St Andrews, provides a more leisurely treatment of metric spaces than is found in books on functional analysis, which are usually written at graduate student level. His presentation is aimed at the applications of the theory to classical algebra and analysis; in particular, the chapter on contraction mappings shows how it provides proof of many of the existence theorems in classical analysis.

Autoren/Hrsg.

Copson, E. T.

Bollobas, Bela

Fulton, W.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

Preface; 1. Introduction; 2. Metric spaces; 3. Open and closed sets; 4. Complete metric spaces; 5. Connected sets; 6. Compactness; 7. Functions and mappings; 8. Some applications; 9. Further developments; Index.