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.

在本文中，我们考虑各种子群的实数和复数矩阵的拓扑商及其与时空结构的联系。这些空间自然被解释为投影点。特别是，我们看非零矩阵的商\(M^*_2({\mathbb {F}})\)通过\(GL_2({\mathbb {F}}),\) \(SL_2({\mathbb {F}}),\) \(O_2({\mathbb {F}}),\)和\(SO_2({\mathbb {F}})\)并证明关于它们的拓扑可分性性质的各种结果。我们讨论了一个有趣的结果，即随着我们所商商的组变小，商的可分离性提高。