Continuous Selections in ${\alpha }$-Convex Metric Spaces
Volume 52 / 2004
Bulletin Polish Acad. Sci. Math. 52 (2004), 303-317
MSC: Primary 54C65; Secondary 54C60.
DOI: 10.4064/ba52-3-10
Abstract
The existence of continuous selections is proved for a class of lower semicontinuous multifunctions whose values are closed convex subsets of a complete metric space equipped with an appropriate notion of convexity. The approach is based on the notion of pseudo-barycenter of an ordered $n$-tuple of points.
