Blowing up points and embedding flat stable planes in the nonorientable compact surface of genus one (Q929988)

The authors consider flat stable planes [compare \textit{B. Polster} and \textit{G. Steinke}, Geometries on Surfaces, Encyclopedia of Mathematics and Its Applications. 84. Cambridge: Cambridge University Press (2001; Zbl 0995.51004)], without assuming connectedness of lines or of the point space. They show that the point set of such a plane is homeomorphic to an open subset of the point set of the real projective plane. In fact, they give two proofs of this result; the first proof uses a construction called blowing up, i.e., replacing a point by its line pencil.