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2 results

  • Acute Triangulation of a Triangle in a General Setting

  • Victor Pambuccian
  • Journal:
    Canadian Mathematical Bulletin / Volume 53 / Issue 3 / 01 September 2010
    Published online by Cambridge University Press:
    20 November 2018, pp. 534-541
    Print publication:
    01 September 2010
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  • We prove that, in ordered plane geometries endowed with a very weak notion of orthogonality, one can always triangulate any triangle into seven acute triangles, and, in case the given triangle is not acute, into no fewer than seven.

  • Compactness in Topological Hjelmslev Planes

  • J. W. Lorimer
  • Journal:
    Canadian Mathematical Bulletin / Volume 27 / Issue 4 / 01 December 1984
    Published online by Cambridge University Press:
    20 November 2018, pp. 423-429
    Print publication:
    01 December 1984
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  • In the theory of ordinary topological affine and projective planes it is known that (1) An affine plane is never compact (2) a locally compact ordered projective plane is compact and archimedean (3) a locally compact connected projective plane is compact and (4) a locally compact projective plane over a coordinate ring with bi-associative multiplication is compact. In this paper we re-examine these results within the theory of topological Hjelmslev Planes and observe that while (1) remains valid (2), (3) and (4) are false. At first glance these negative results seem to suggest we are working in too general a setting. However a closer examination reveals that the absence of compactness in our setting is a natural and expected feature which in no way precludes the possibility of obtaining significant results.