The Open Graph Theorem for Correspondences: A New Proof and Some Applications

Galeazzo Impicciatore, Francesco Ruscitti

Department of Economics and Law, University La Sapienza, Rome, Italy.
Department of Political and Social Sciences, John Cabot University, Rome, Italy.

DOI: 10.4236/tel.[phone]                

Abstract

It is known that a correspondence from a topological space to a Euclidean space, with open and convex upper sections, has an open graph if and only if it is lower hemicontinuous. We refer to this result as the open graph theorem. We provide a new and simple proof of the open graph theorem. We also show that the open graph theorem leads to novel results on the existence of constant selections and fixed points for correspondences with non-compact and non-convex domain. Finally, we present an economic application of our results to a principal-agent model.

Keywords

Open Graph Theorem; Lower Hemicontinuity; Constant Selections; Fixed Points; Support of a Measure

Conflicts of Interest

The authors declare no conflicts of interest.

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