Analyse. I : théorie des ensembles et topologie / Laurent Schwartz

Auteur: Schwartz, Laurent (1915-2002) - AuteurAuteur secondaire : Zizi, Khelifa - CollaborateurType de document: MonographieCollection: Enseignement des sciences ; 42Langue: françaisPays: FranceÉditeur: Paris : Hermann, 1991Description: 1 vol. (404 p.) ; 24 cm ISBN: 9782705661618 ; br. Note: 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.Bibliographie: Bibliogr. p. [397-398]. Index. Sujets MSC: 54-01 General topology -- Instructional exposition (textbooks, tutorial papers, etc.)
46-01 Functional analysis -- Instructional exposition (textbooks, tutorial papers, etc.)
03-01 Mathematical logic and foundations -- Instructional exposition (textbooks, tutorial papers, etc.)
Location Call Number Status Date Due
Salle E 10767-02 / Agreg-SCD SCH (Browse Shelf) Consultation sur place

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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