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Über die Fortsetzung einer Anordnung der affinen Klingenbergschen Ebene in einer Anordnung der projektiven Klingenbergschen Ebene. (German) Zbl 0545.51011

This paper continues the author’s earlier work [Čas. Pestovani. Mat. 106, 138–155 (1981; Zbl 0475.51003), and Acta Univ. Palacki. Olomuc., Fac. Rerum Nat. 73, Math. 21, 9–31 (1982; Zbl 0515.51013)] on ordered Klingenberg planes. The main theorem gives necessary and sufficient conditions (A1)–(A4) for an ordered affine Klingenberg plane to be embeddable in an ordered projective Klingenberg plane. In both planes the neighbourhoods are supposed to be convex with respect to the given order. Some of the conditions and the proof of that theorem are highly technical.

MSC:

51G05 Ordered geometries (ordered incidence structures, etc.)
51C05 Ring geometry (Hjelmslev, Barbilian, etc.)
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References:

[1] Kunze M.: Angeordnete Hjelmslevsche Geometrie. Dissertation, Christian-Albrechts-Universität zu Kiel 1975. · Zbl 0462.51011
[2] Machala F.: Über Mengen mit Trennrelationen. Acta Univ. Pal. Olomucensis Tom 69, 1981, 5-22. · Zbl 0478.06001
[3] Machala F.: Über angeordnete affine Klingenbergsche Ebenen, die sich in projektive Klingenbergsche Ebene einbetten lassen. Acta Univ. Pal. Olomucensis Tom 73, 1982, 9-31. · Zbl 0515.51013
[4] Machala F.: Fastgeordnete und geordnete affine Klingenbergsche Ebenen. Čas. pro pěst. mat. 106 (1981), 138-155. · Zbl 0475.51003
[5] Pickert G.: Projektive Ebenen. Springer-Verlag Berlin, Heidelberg, New York 1975. · Zbl 0307.50001
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