Continuous Selections III

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Annals of Mathematics is collaborating with JSTOR to digitize, preserve and extend access to Annals of Mathematics.

The geometry of the critical set of nonlinear periodic Sturm–Liouville operators

“…Extending the diffeomorphism to the complement is then easy. To insure that the hypothesis of Proposition 5.5 holds, however, we need Michael's continuous selection theorem (the main result in [15]), which we state below in the special situation we use.…”

“…The ingredients are combined in Section 6 to complete the proof of Theorem 1; we express our thanks to S. Ferry for providing first the arguments and afterwards directing us to the appropriate Ref. [15] for what we call here Michael's theorem (Fact 2).…”

By Their Fruits Ye Shall Know Them: Some Remarks on the Interaction of General Topology with Other Areas of Mathematics

“…The work on compactifications in the 1950's culminated in the publication of the beautiful book [76] by Gillman and Jerison. Michael [123,124,125] developed his theory of continuous selections. For more information, see e.g.…”

Continuous approximate solutions in parametric optimization

“…In a sense, the conditions were already present in the convex setting, since Michael's selection theorems [23][24][25][26] imply fibration conditions. It was not necessary to mention these explicitly, however, since continuous solutions could be obtained directly from the multifunction statement of Michael's theorems.…”