Metric spaces / E. T. CopsonType de document : MonographieCollection : Cambridge tracts in mathematics and mathematical physics, 57Langue : anglais.Pays: Grande Bretagne.Éditeur : London : Cambridge University Press, 1968Description : 1 vol. (143 p.) ; 23 cmISBN: 9780521047227.ISSN: 0068-6824.Bibliographie : Index.Sujet MSC : 54-01, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to general topology
54E35, General topology - Topological spaces with richer structures, Metric spaces, metrizability
54H25, Connections of general topology with other structures, applications, Fixed-point and coincidence theoremsEn-ligne : MathSciNet | Zentralblatt Item type: Monographie
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Author's preface: "This book, based on lectures given in the University of St. Andrews, is intended to give honours students the background and training necessary before they start to study functional analysis.
"There are many books on functional analysis; and some of them seem to go over the preliminaries to the subject far too quickly. The aim here is to provide a more leisurely approach to the theory of the topology of metric spaces, a subject which is not only the basis of functional analysis but also unifies many branches of classical analysis. The applications of the theory in Chapter 8 to problems in classical algebra and analysis show how much can be done without ever defining a normed vector space, a Banach space or a Hilbert space. Chapter headings: (1) Introduction; (2) Metric spaces; (3) Open and closed sets; (4) Complete metric spaces; (5) Connected sets; (6) Compactness; (7) Functions and mappings; (8) Some applications; (9) Further developments. (MathSciNet)