In a 1983 paper, Yannelis-Prabhakar rely on Michael's selection theorem to guarantee a continuous selection in the context of the existence of maximal elements and equilibria in abstract economies. In this tribute to Nicholas Yannelis, we root this paper in
- Chapter II of Yannelis' 1983 Rochester Ph.D. dissertation, and identify its pioneering application of the paracompactness condition to current and ongoing work of Yannelis and his co-authors, and to mathematical economics more generally. We move beyond the literature to provide a necessary and sufficient condition for upper semi-continuous local and global selections of correspondences, and to provide application to five domains of Yannelis' interests: Berge's maximum theorem, the Gale-Nikaido-Debreu lemma, the Gale-McKenzie survival assumption, Shafer's non-transitive setting, and the Anderson-Khan-Rashid approximate existence theorem. The last resonates with
- Chapter VI of the Yannelis' dissertation.