Metric Spaces

2007
ISBN: 978-1-84628-369-7
Verlag: Springer

Buch, Englisch, 304 Seiten, Format (B × H): 178 mm x 254 mm, Gewicht: 1260 g

Reihe: Springer Undergraduate Mathematics Series

The abstract concepts of metric spaces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective on ideas familiar from the analysis of a real line. Rather than passing quickly from the definition of a metric to the more abstract concepts of convergence and continuity, the author takes the concrete notion of distance as far as possible, illustrating the text with examples and naturally arising questions.

The book provides a thorough exposition of all the standard necessary results of the theory and, in addition, includes selected topics not normally found in introductory books, such as: the Tietze Extension Theorem; the Hausdorff metric and its completeness; and the existence of curves of minimum length.

With its many examples, careful illustrations, and full solutions to selected exercises, this book provides a gentle introduction that is ideal for self-study and an excellent preparation for applications.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

O'Searcoid, Mícheál

Ó Searcóid, Mícheál

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie

Inhaltsverzeichnis

Metrics.- Distance.- Boundary.- Open, Closed and Dense Subsets.- Balls.- Convergence.- Bounds.- Continuity.- Uniform Continuity.- Completeness.- Connectedness.- Compactness.- Equivalence.

Über Autor(innen)

Mícheál Ó Searcóid is author of another, higher-level, SUMS book, Elements of Abstract Analysis, 1-85233-424-X, published November 2001, sales (as of June 2005): 1051 (ROW: 634; US: 417).