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Differential geometry. Global analysis --- 515.1 --- Topology --- 515.1 Topology --- Differentiable mappings --- Singularities (Mathematics) --- Applications différentiables --- Singularités (Mathématiques) --- Applications différentiables --- Singularités (mathématiques) --- Differential topology --- Topologie différentielle --- Singularités (mathématiques) --- Topologie différentielle --- Analyse sur une variété

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In winter 71/72 I held a seminar on general equilibrium theory for a jOint group of students in mathematics and in econo­ mics at the university of Bonn , w.Germany1~ The economists , how­ ever , had a mathematical background well above the average • Most of the material treated in that seminar is described in these notes. The connection between smooth preferences and smooth demand func­ tions [ see Debreu (1972) ] and regular economies based on agents with smooth preferences are not presented here • Some pedagogical difficulties arose from the fact that elementary knowledge of algebraic topology is not assumed although it is helpful and indeed necessary to make some arguments precise • It is only a minor restriction , at present , that functional ana­ lysis is not used • But with the development of the theory more economic questions will be considered in their natural infinite dimensional setting • Economic knowledge is not required , but especially a reader without economic background will gain much by reading Debreu's classic "Theory of Value" (1959) • Although the formulation of our economic problem uses a map between Euclidean spaces only , we shall also consider ma- folds • Manifolds appear in our situation because inverse images under differentiable mappings between Euclidean spaces are very often differentiable manifolds • ( Under differentiability assump­ tions , for instance , the graph of the equilibrium set correspon­.

Topology --- Walras, Léon --- Economics, Mathematical --- 330.105 --- Wiskundige economie. Wiskundige methoden in de economie --- Business & Economics --- Economic Theory --- 330.105 Wiskundige economie. Wiskundige methoden in de economie --- Walras, Léon, --- Differentiable mappings --- Applications différentiables --- Singularities (Mathematics) --- Singularités (mathématiques) --- Critical point theory (Mathematical analysis) --- Points critiques, Théorie des (analyse mathématique) --- Differential topology --- Topologie différentielle --- Singularités (mathématiques) --- Topologie différentielle --- Differentiable mappings. --- Applications différentiables --- Points critiques, Théorie des (analyse mathématique) --- Point fixe, Théorème du --- Walras, Léon, - 1834-1910. --- Economie mathematique --- Equilibre (economie politique) --- Modeles mathematiques