Book Review: Metric spaces, convexity, and nonpositive curvature

Abstract

Introduction : some historical markers -- 1. Lengths of paths in metric spaces -- 2. Length spaces and geodesic spaces -- 3. Maps between metric spaces -- 4. Distances -- 5. Convexity in vector spaces -- 6. Convex functions -- 7. Strictly convex normed vector spaces -- 8. Busemann spaces -- 9. Locally convex spaces -- 10. Asymptotic rays and the visual boundary -- 11. Isometries -- 12. Busemann functions, co-rays and horospheres.