Ends of surface geometries, revisited
Let \({\mathcal E} = ({\mathcal S}, {\mathcal L})\) denote a stable plane [cf. chapter 23 by \textit{Th. Grundhöfer} and the author in F. Buekenhout (ed.), Handbook of incidence geometry, 1255-1324 (1995; Zbl 0824.51011)] for the definition and generalizations of this concept. If the point set \({\mathcal S}\) is a surface and the lines from \({\mathcal L}\) are connected, then the author proves without the assumption of finite connectivity (which in addition had been made by \textit{H. Salzmann} [Pac. J. Math. 29, 397-402 (1969; Zbl 0181.23301)] to derive the same theorem) that \({\mathcal S}\) is either the open disk, or the compact surface of characteristic 1, or the Möbius strip. The corresponding line spaces are also described under the weakened assumptions. Crucial arguments are provided by the use of the Freudenthal compactification of \({\mathcal S}\) [cf. \textit{J. R. Isbell}, `Uniform spaces' (1964; Zbl 0124.15601)].
scientific article; zbMATH DE number 826778
scientific article