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Locally Compact Hjelmslev Planes and Rings

Published online by Cambridge University Press:  20 November 2018

J. W. Lorimer
J. W. Lorimer*
Affiliation:
University of Toronto, Toronto, Ontario
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Affine and projective Hjelmslev planes are generalizations of ordinary affine and projective planes where two points (lines) may be joined by (may intersect in) more than one line (point). The elements involved in multiple joinings or intersections are neighbours, and the neighbour relations on points respectively lines are equivalence relations whose quotient spaces define an ordinary affine or projective plane called the canonical image of the Hjelmslev plane. An affine or projective Hjelmslev plane is a topological plane (briefly a TH-plane and specifically a TAH-plane respectively a TPH-plane) if its point and line sets are topological spaces so that the joining of non-neighbouring points, the intersection of non-neighbouring lines and (in the affine case) parallelism are continuous maps, and the neighbour relations are closed.

In this paper we continue our investigation of such planes initiated by the author in [38] and [39].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 4 , 01 August 1981 , pp. 988 - 1021
Copyright
Copyright © Canadian Mathematical Society 1981

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