ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. LXXIV, 1 (2005)
p. 133 - 141

Continuous selections for Lipschitz multifunctions
I. Kupka

Abstract.  In [11] an example presented a Hausdorff continuous, u.s.c. and l.s.c. multifunction from $\langle-1,0\rangle$ to $\Bbb R$ which had no continuous selection. The multifunction was not locally Lipschitz. In this paper we show that a locally Lipschitz multifunction from $\Bbb R$ to a Banach space, which has ''locally finitely dimensional closed values does have a continuous selection.

Keywords: Continuous selection, Lipschitz multifunction.

AMS Subject classification:  Primary: 54C65; Secondary: 54C30.