Real Algebraic and Analytic Geometry
Submission: 2016, April 14.
Let R be a real closed field and let some o-minimal structure extending R be given. Let F : A -> R^m be a definable multivalued lower semicontinuous mapping with nonempty definably connected values defined on a definable subset A of R^n of dimension 1 (A can be identified with a finite graph immersed in R^n ). Then F admits a definable continuous selection.
Mathematics Subject Classification (2010): 14P10, 54C60, 54C65, 32B20, 49J53.
Keywords and Phrases: Michael's selection theorem, o-minimal structure, finite graph.
Full text, 3p.: pdf 138k.