Topological properties of locally compact connected Minkowski planes and their derived affine planes (Q919273)

Let \({\mathcal M}\) be a topological Minkowski plane. The author closes gaps in the literature by proving: If the point space P is locally compact and connected, then it is compact. If P is finite-dimensional, then: Every derived affine plane is a topological affine plane. P is 2- or 4-dimensional, circles are homeomorphic to the spheres \(S_ 1\) resp. \(S_ 2\), and P is homeomorphic to \(S_ 1\times S_ 1\) resp. \(S_ 2\times S_ 2\).