Hyperbolic geometry for non-differential topologists

Abstract

A soft presentation of hyperbolic spaces (as metric spaces), free of dierential apparatus, is offered. Fifth Euclid's postulate in such spaces is overthrown and, among other things, it is proved that spheres (equipped with great-circle distances) and hyperbolic and Euclidean spaces are the only locally compact geodesic (i.e., convex) metric spaces that are three-point homogeneous.