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

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