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

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