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The Open Graph Theorem for Correspondences: A New Proof and Some Applications
Impicciatore, Galeazzo Ruscitti, Francesco
Impicciatore, Galeazzo
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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.
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Date
2012
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Keywords
Open graph theorem, Lower hemicontinuit, Constant selection, Fixed points, Support of a measure
Citation
Impicciatore, Galeazzo, and Francesco Ruscitti. “The Open Graph Theorem for Correspondences: A New Proof and Some Applications.” Theoretical Economics Letters 2 (3): 270–73. 2012.