Michael selection theorem

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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 : XE a lower hemicontinuous multivalued map with nonempty convex closed values. Then there exists a continuous selection f : XE 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[edit]


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  • S.Hu, N.Papageorgiou Handbook of multivalued analysis. Vol. I Kluwer