Analyse, I, théorie des ensembles et topologie / Laurent Schwartz ; avec la collaboration de K. Zizi

Auteur principal : Schwartz, Laurent, 1915-2002, AuteurAuteur secondaire : Zizi, Khelifa, CollaborateurType de document : MonographieCollection : Enseignement des sciences, 42Langue : français.Pays: France.Mention d'édition: nouveau tirageÉditeur : Paris : Hermann, 1995Description : 1 vol. (404 p.) ; 24 cmISBN: 2705661618.ISSN: 0768-0341.Bibliographie : Bibliogr. p. [397-398]. Index.Sujet MSC : 54-01, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to general topology
46-01, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis
03-01, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations
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Contents: Chapter I. Set theory: §1 Some elements of classical logic; §2 Set theory – the five primary axioms; §3 Mappings, family, product of a family of sets, axiom of choice; §4 The natural numbers – the axiom of infinity; §5 Quotient sets; §6 Ordered sets; §7 Infinite sets – operations on infinite sets; §8 Ordinal and cardinal numbers. Chapter II. Topology: §1 Metric spaces; §2 Topological spaces; §3 Continuous and semi-continuous functions – homeomorphisms; §4 Metric spaces and topological spaces; §5 Compact spaces – elementary properties; §6 Convergence, limits, sequences and filters; §7 Properties of continuous functions on a compact space; §8 Locally compact spaces; §9 Connected spaces, arc-connected spaces, locally connected spaces; §10 Complete metric spaces; §11 Elementary theory of normed linear spaces and Banach spaces; §12 Series in normed linear spaces; §13 Function spaces – pointwise and uniform convergence; §14 Elementary spectral theory (including the Gel'fand-Najmark theorem and the Bochner-Raikov theorem); §15 Infinite products of numbers or of real or complex functions.

Bibliogr. p. [397-398]. Index

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