Egbert Dierker

Die von Karl Menger und seinen Mitarbeitern (darunter Kurt Godel) herausgegebenen Ergebnisse eines Mathematischen Kolloquiums zahlen zu den wichtigsten Quellenwerken der Wissenschafts- und Geistesgeschichte der Zwischenkriegszeit, mit bahnbrechenden Beitragen von Menger, Godel, Tarski, Wald, John von Neumann und vielen anderen. In diesem Band liegt der Inhalt erstmals gesammelt vor. Der Nobelpreistrager Gerard Debreu schrieb die Einleitung, die Kommentare wurden vom Logiker und Godel-Biographen John Dawson jr., dem Topologen Ryszard Engelking und dem Wirtschaftstheoretiker Werner Hildenbrand verfasst.Auberdem enthalt der Band einen biographischen Aufsatz uber Karl Menger sowie einen von Menger verfassten Uberblick uber die wichtigsten topologischen und geometrischen Arbeiten des Kolloquiums.

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