Michael selection theorem
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- 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
- Aumann measurable selection theorem
- Bressan-Colombo directionally continuous selection theorem
- Castaing representation theorem
- Fryszkowski decomposable map selection
- Helly's selection theorem
- Kuratowski, Ryll-Nardzewski measurable selection theorem
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- D.Repovs and P.V.Semenov, Ernest Michael and theory of continuous selections, Topol. Appl. 155:8 (2008), 755-763.
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- S.Hu, N.Papageorgiou Handbook of multivalued analysis. Vol. I Kluwer