Affiliation:
1. Instytut Matematyki, Wydział Matematyki i Informatyki, Uniwersytet Jagielloński, ul. Łojasiewicza 6 , Kraków , POLAND
Abstract
Abstract
A soft presentation of hyperbolic spaces (as metric spaces), free of differential 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.