Michael selection theorem
- Michael selection theorem
-
In functional analysis, a branch of mathematics, the most popular version of the Michael selection theorem, named after Ernest Michael, states the following:
- Let E be a Banach space, X a paracompact space and φ : X → E a lower semicontinuous multivalued map with nonempty convex closed values. Then there exists a continuous selection f : X → E of φ.
- Conversely, if any lower semicontinuous multimap from topological space X to a Banach space, with nonempty convex closed values admits continuous selection, then X is paracompact. This provides another characterization for paracompactness.
Other selection theorems
- Zero-dimensional Michael selection theorem
- Castaing representation theorem
- Bressan-Colombo directionally continuous selection theorem
- Fryszkowski decomposable map selection
- Aumann measurable selection theorem
- Kuratowski, Ryll-Nardzewski measurable selection theorem
References
- Michael, Ernest (1956), "Continuous selections. I", Annals of Mathematics. Second Series (Annals of Mathematics) 63 (2): 361–382, doi:10.2307/1969615, JSTOR 1969615, MR0077107
- D.Repovs, P.V.Semenov,Ernest Michael and theory of continuous selections" arXiv:0803.4473v1
- Jean-Pierre Aubin, Arrigo Cellina Differential Inclusions, Set-Valued Maps And Viability Theory, Grundl. der Math. Wiss., vol. 264, Springer - Verlag, Berlin, 1984
- J.-P. Aubin and H. Frankowska Set-Valued Analysis, Birkh¨auser, Basel, 1990
- Klaus Deimling Multivalued Differential Equations, Walter de Gruyter, 1992
- Aliprantis, Kim C. Border Infinite dimensional analysis. Hitchhiker's guide Springer
- S.Hu, N.Papageorgiou Handbook of multivalued analysis. Vol. I Kluwer
Categories:
- Continuous mappings
- Properties of topological spaces
- Theorems in functional analysis
- Compactness theorems
Wikimedia Foundation.
2010.
Look at other dictionaries:
Michael Szenberg — is the distinguished professor of economics and chairman of the finance and economics department at Pace University’s Lubin School of Business.[1] He is editor of The American Economist.[2][3] Contents 1 Life … Wikipedia
Ernest Michael — is an American mathematician who is best known for Michael selection theorem, which he proved in harv|Michael|1956. He received his Ph.D. from the University of Chicago in 1951. He wrote his dissertation on Locally m convex algebras under the… … Wikipedia
Max Michael Munk — Max Michael Munk, 1926 in seinem Büro in Langley Max Michael Munk (* 22. Oktober 1890 in Hamburg[1]; † 1986) war ein deutsch amerikanischer Aeronautiker.[2] … Deutsch Wikipedia
Bohr–Mollerup theorem — In mathematical analysis, the Bohr–Mollerup theorem is named after the Danish mathematicians Harald Bohr and Johannes Mollerup, who proved it. The theorem characterizes the gamma function, defined for x > 0 by:Gamma(x)=int 0^infty t^{x 1} e^{… … Wikipedia
Multivalued function — This diagram does not represent a true function, because the element 3 in X is associated with two elements, b and c, in Y. In mathematics, a multivalued function (shortly: multifunction, other names: set valued function, set valued map, multi… … Wikipedia
List of mathematics articles (M) — NOTOC M M estimator M group M matrix M separation M set M. C. Escher s legacy M. Riesz extension theorem M/M/1 model Maass wave form Mac Lane s planarity criterion Macaulay brackets Macbeath surface MacCormack method Macdonald polynomial Machin… … Wikipedia
Hemicontinuity — In mathematics, the concept of continuity as it is defined for single valued functions is not immediately extendible to multi valued mappings or correspondences. In order to derive a more generalized definition, the dual concepts of upper… … Wikipedia
Paracompact space — In mathematics, a paracompact space is a topological space in which every open cover admits a locally finite open refinement. Paracompact spaces are sometimes also required to be Hausdorff. Paracompact spaces were introduced by Dieudonné (1944).… … Wikipedia
Bounded variation — In mathematical analysis, a function of bounded variation refers to a real valued function whose total variation is bounded (finite): the graph of a function having this property is well behaved in a precise sense. For a continuous function of a… … Wikipedia
nature, philosophy of — Introduction the discipline that investigates substantive issues regarding the actual features of nature as a reality. The discussion here is divided into two parts: the philosophy of physics and the philosophy of biology. In this… … Universalium
