Metric Spaces

Buch | Softcover
304 Seiten
2006
Springer London Ltd (Verlag)
978-1-84628-369-7 (ISBN)

Lese- und Medienproben

Metric Spaces - Mícheál O'Searcoid
40,65 inkl. MwSt
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.

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).

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

Erscheint lt. Verlag 8.9.2006
Reihe/Serie Springer Undergraduate Mathematics Series
Springer Undergraduate Mathematics Series
Zusatzinfo 102 Illustrations, black and white; XX, 304 p. 102 illus.
Verlagsort England
Sprache englisch
Maße 178 x 254 mm
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Geometrie / Topologie
Schlagworte Continuity • convergence • Distance • Metric Spaces • Metric space theory • Open sets
ISBN-10 1-84628-369-8 / 1846283698
ISBN-13 978-1-84628-369-7 / 9781846283697
Zustand Neuware
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