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.

我们在1983年罗彻斯特博士的第二章中对尼古拉斯·扬内利斯（Nicholas Yannelis）表示敬意。论文，以及他在1983年与Prabhakar的论文中：这项工作加强了迈克尔连续选择定理的低半连续假设，以打开下部，并导致在超紧实空间上定义的对应性与Hausdorff线性拓扑空间上的值相对应。我们超越了文献，为上半连续的局部和全局对应选择提供了必要和充分的条件，并将我们的结果应用于Yannelis贡献的四个领域：Berge的最大定理，G​​ale–Nikaido–Debreu引理，Sonnenschein -Shafer非及物设置，以及Anderson-Khan-Rashid近似存在定理。最后一点也与Yannelis论文的第六章产生了共鸣，超紧凑性为他目前和正在进行的数学经济学工作创造了条件。