Robert Magnus: Metric Spaces | Taschenbuch

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

Rückseite: 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

In a long career as a university teacher Robert Magnus has taught most subjects in the area of analysis, including ordinary differential equations both at undergraduate and postgraduate level. He has published papers in areas allied to analysis, including non-linear partial differential equations.

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 , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
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
Einband:	Kartoniert / Broschiert
Autor:	Magnus, Robert
Auflage:	1st edition 2022
Hersteller:	Springer Springer International Publishing AG Springer Undergraduate Mathematics Series
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 15 mm
Von/Mit:	Robert Magnus
Erscheinungsdatum:	17.03.2022
Gewicht:	0,406 kg