Projective Points Over Matrices and Their Separability Properties

Abstract

In this article we consider topological quotients of real and complex matrices by various subgroups and their connections to spacetime structures. These spaces are naturally interpreted as projective points. In particular, we look at quotients of nonzero matrices M^*_2({mathbb {F}}) by GL_2({mathbb {F}}),SL_2({mathbb {F}}),O_2({mathbb {F}}), and SO_2({mathbb {F}}) and prove various results about their topological separability properties. We discuss the interesting result that, as the group we quotient by gets smaller, the separability properties of the quotient improve.