Topological Methods in Walrasian Economics

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