Una demostración constructiva de un homeomorfismo entre P3 y SO(3)

Abstract

The paper gives a very elementary proof of the well-known result that the projective space P3 is homeomorphic to the special orthogonal Lie group SO(3). The proof uses only linear algebra, elementary topology and elementary affine geometry. One of its motivations is the theory developed in the classical book of M. L. Curtis [Matrix groups, Springer, New York, 1979; MR0550439 (81c:22001)]. The paper is also very useful for young students in mathematics to become initiated in Lie theory and its applications.