Real Algebraic and Analytic Geometry |

Michael's Theorem for a Mapping Definable in an O-Minimal Structure on a Set of Dimension 1.

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Submission: 2016, April 14.

*Abstract:
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.:
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