The Yannelis–Prabhakar theorem on upper semi-continuous selections in paracompact spaces: extensions and applications

M. Khan and Metin Uyanık

Economic Theory, 2021, vol. 71, issue 3, No 2, 799-840

Abstract: Abstract We root this tribute to Nicholas Yannelis in Chapter II of his 1983 Rochester Ph.D. dissertation, and in his 1983 paper with Prabhakar: this work strengthens the lower semicontinuity assumption of Michael’s continuous selection theorem to open lower sections, and leads to correspondences defined on a paracompact space with values on a Hausdorff linear topological space. We move beyond the literature to provide a necessary and sufficient condition for upper semi-continuous local and global selections of correspondences, and apply our result to four domains of Yannelis’ contributions: Berge’s maximum theorem, the Gale–Nikaido–Debreu lemma, the Sonnenschein–Shafer non-transitive setting, and the Anderson–Khan–Rashid approximate existence theorem. The last also resonates with Chapter VI of Yannelis’ dissertation, and allows a more general framing of the pioneering application of the paracompactness condition to his current and ongoing work in mathematical economics.

Keywords: YP selection theorem; Paracompactness; Local selection; Global selection; Berge’s maximum theorem; BMY map; GND lemma; AKR Approximate equilibrium; 46A03; 54C65; 54H25; 91B42; 91B50 (search for similar items in EconPapers)
JEL-codes: C02 D11 D51 D62 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (6)

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Working Paper: The Yannelis-Prabhakar Theorem on Upper Semi-Continuous Selections in Paracompact Spaces: Extensions and Applications (2020)
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DOI: 10.1007/s00199-021-01359-4

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