A NOTE ON METRIC SPACES WITH CONTINUOUS MIDPOINTS

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.