Michael's selection theorem for a mapping definable in an O-minimal structure defined on a set of dimesion 1
Keywords
Michael's selection theorem, o-minimal structure, finite graphAbstract
Let $R$ be a real closed field and let some o-minimal structure extending $R$ be given. Let $F\colon X \rightrightarrows R^m$ be a definable multivalued lower semicontinuous mapping with nonempty definably connected values defined on a definable subset $X$ of $R^n$ of dimension $1$ ($X$ can be identified with a finite graph immersed in $R^n$). Then $F$ admits a definable continuous selection.Published
2017-01-11
How to Cite
1.
CZAPLA, Małgorzata and PAWŁUCKI, Wiesław. Michael’s selection theorem for a mapping definable in an O-minimal structure defined on a set of dimesion 1. Topological Methods in Nonlinear Analysis. Online. 11 January 2017. Vol. 49, no. 1, pp. 377 - 380. [Accessed 14 December 2024].
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