Metric Spaces

Satish Shirali, Harkrishan L. Vasudeva

222 pages, parution le 06/10/2005

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Résumé

This volume provides a complete introduction to metric space theory for undergraduates. It covers the topology of metric spaces, continuity, connectedness, compactness and product spaces, and includes results such as the Tietze-Urysohn extension theorem, Picard's theorem on ordinary differential equations, and the set of discontinuities of the pointwise limit of a sequence of continuous functions. Key features include:

a full chapter on product metric spaces, including a proof of Tychonoff's Theorem
a wealth of examples and counter-examples from real analysis, sequence spaces and spaces of continuous functions
numerous exercises - with solutions to most of them - to test understanding.

The only prerequisite is a familiarity with the basics of real analysis: the authors take care to ensure that no prior knowledge of measure theory, Banach spaces or Hilbert spaces is assumed. The material is developed at a leisurely pace and applications of the theory are discussed throughout, making this book ideal as a classroom text for third- and fourth-year undergraduates or as a self-study resource for graduate students and researchers.

Sommaire

Preliminaries
Basic Concepts
Topology of a Metric Space
Continuity
Connected Spaces
Compact Spaces
Product Spaces
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Satish Shirali, Harkrishan L. Vasudeva
Parution	06/10/2005
Nb. de pages	222
Format	17,5 x 23,5
Couverture	Broché
Poids	386g
Intérieur	Noir et Blanc
EAN13	9781852339227
ISBN13	978-1-85233-922-7