%0 Journal Article %T A NOTE ON METRIC SPACES WITH CONTINUOUS MIDPOINTS %A Charles Horvath %J Mathematics and its Applications : Annals of the Academy of Romanian Scientists %D 2010 %I Academy of Romanian Scientists Publishing House %X Under suitable, but natural, assumptions continuous midpointspaces are absolute retracts; Browder, Michael or Cellina likecontinuous selection theorems hold; bounded closed convex sets havethe fixed point property for nonexpansive maps. Hyperconvex metricspaces, Cartan-Hadamard manifolds and more generally Hadamardspaces or metric spaces with non positive curvature in the sense ofBusemann are continuous midpoint spaces. %K selections %K fixed points %K geodesic convexity %K Busemann spaces %K cat(0) spaces %K hyperconvex spaces %U http://www.mathematics-and-its-applications.com/preview/january/data/3_horvath.pdf