### Continuous selections via geodesics

#### Abstract

Some continuous selection results for a class of nonconvex-valued maps

are obtained. One of them contains Michael's theorem, in the case of a

Hilbert codomain. Methods of nonsmooth analysis

and $\Gamma$-convergence are used.

are obtained. One of them contains Michael's theorem, in the case of a

Hilbert codomain. Methods of nonsmooth analysis

and $\Gamma$-convergence are used.

#### Keywords

Distance functions; metric projection; continuous dependence of geodesics; $\varphi$-convex sets

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