Uniformly continuous selections in Fréchet spaces (Q1086876)

The author gives a sufficient existence condition for a uniformly continuous selection of a uniformly continuous multifunction with closed convex bounded images in a Fréchet space. The Corollary 1 of this note generalizes Theorem 3.1 c of \textit{J. R. Isbell} [Pac. J. Math. 11, 609- 648 (1961; Zbl 0109.154)] and Theorem 8 of \textit{J. Lindenstrauss} [Mich. Math. J. 11, 263-281 (1964; Zbl 0195.428)].