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Existence of maximal elements and equilibria in linear topological spaces. (English) Zbl 0536.90019
Summary: We present some mathematical theorems which are used to generalize previous results on the existence of maximal elements and of equilibrium. Our main theorem in this paper is a new existence proof for an equilibrium in an abstract economy, which is closely related to a previous result of A. Borglin and H. Keiding [ibid. 3, 313- 316 (1976; Zbl 0349.90157)] and W. Shafer and H. Sonnenschein [ibid. 2, 345-348 (1975; Zbl 0312.90062)] but allows for an infinite number of commodities and a countably infinite number of agents.

MSC:
91B50General equilibrium theory in economics
54H25Fixed-point and coincidence theorems in topological spaces