Ordered affine Hjelmslev planes

Baker, C. A.

doi:10.1007/bf01225282

J Geom

1984

DOI: 10.1007/bf01225282

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Ordered affine Hjelmslev planes

C. A. Baker

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Coordinate rings of topological Klingenberg planes I: The affine perspective

Baker

Lorimer

1995

Geom Dedicata

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Abstract. Although the coordinate ternary field of a topological affine plane is topological, the converse does not hold. However, an affine plane is topological precisely when its coordinate biternary fields are topological. We extend this result to topological biternary rings and their topological affine Klingenberg planes. Then we examine the locally compact situation. Finally, following the ideas of Knarr and Weigand, we show that in certain circumstances, the continuity of the ternary operators is sufficient to ensure that the biternary ring is topological. This facilitates the construction of locally compact, locally connected affine Klingenberg planes.Mathematics Subject Classifications (1991): 51E 15, 54H 13.

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Coordinate rings of topological Klingenberg planes I: The affine perspective

Baker

Lorimer

1995

Geom Dedicata

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The axiomatics of ordered geometry

Pambuccian

2011

Expositiones Mathematicae

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Ordered affine Hjelmslev planes

Cited by 2 publications

References 10 publications

Coordinate rings of topological Klingenberg planes I: The affine perspective

Coordinate rings of topological Klingenberg planes I: The affine perspective

The axiomatics of ordered geometry

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