Robert Magnus: Metric Spaces | Taschenbuch

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Cover: 9783030949457 | Metric Spaces | A Companion to Analysis | Robert Magnus | Taschenbuch

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Sprache: Englisch

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Beschreibung

This textbook presents the theory of Metric Spaces necessary for studying analysis beyond one real variable. Rich in examples, exercises and motivation, it provides a careful and clear exposition at a pace appropriate to the material.

The book covers the main topics of metric space theory that the student of analysis is likely to need. Starting with an overview defining the principal examples of metric spaces in analysis (chapter 1), it turns to the basic theory (chapter 2) covering open and closed sets, convergence, completeness and continuity (including a treatment of continuous linear mappings). There is also a brief dive into general topology, showing how metric spaces fit into a wider theory. The following chapter is devoted to proving the completeness of the classical spaces. The text then embarks on a study of spaces with important special properties. Compact spaces, separable spaces, complete spaces and connected spaces each have a chapter devoted to them. A particular feature of the book is the occasional excursion into analysis. Examples include the Mazur¿Ulam theorem, Picard¿s theorem on existence of solutions to ordinary differential equations, and space filling curves.

This text will be useful to all undergraduate students of mathematics, especially those who require metric space concepts for topics such as multivariate analysis, differential equations, complex analysis, functional analysis, and topology. It includes a large number of exercises, varying from routine to challenging. The prerequisites are a first course in real analysis of one real variable, an acquaintance with set theory, and some experience with rigorous proofs.

Über den Autor

Robert Magnus was born in the UK and studied mathematics at the Universities of Cambridge and Sussex. He has taught nearly all subjects associated with analysis and has published papers in the areas of bifurcation theory, catastrophe theory, analytic operator functions and nonlinear partial differential equations. Since 1977 he has lived and worked in Iceland.

Zusammenfassung

Provides a lucid and clear exposition which includes additional motivation and explanation for delicate points

Presents metric spaces as a tool for advanced analysis, topology and related subjects

Includes many exercises with hints

Inhaltsverzeichnis

- 1. Metric Spaces. - 2. Basic Theory of Metric Spaces. - 3. Completeness of the Classical Spaces. - 4. Compact Spaces. - 5. Separable Spaces. - 6. Properties of Complete Spaces. - 7. Connected Spaces. - Afterword.

Details

Erscheinungsjahr:	2022
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	264
Reihe:	Springer Undergraduate Mathematics Series
Inhalt:	xix 244 S. 10 s/w Illustr. 1 farbige Illustr. 244 p. 11 illus. 1 illus. in color.
ISBN-13:	9783030949457
ISBN-10:	3030949451
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Magnus, Robert
Auflage:	1st ed. 2022
Hersteller:	Springer International Publishing Springer Undergraduate Mathematics Series
Maße:	235 x 155 x 15 mm
Von/Mit:	Robert Magnus
Erscheinungsdatum:	17.03.2022
Gewicht:	0,406 kg

preigu-id: 120929036