Geometry on the lines of spine spaces
Spine spaces can be considered as fragments of a projective Grassmann space. We prove that the structure of lines together with a binary coplanarity relation, as well as with the binary relation of being in one pencil of lines, is a sufficient system of primitive notions for these geometries. It is also shown that, over a spine space, the geometry of pencils of lines can be reconstructed in terms of the two binary relations.
KeywordsGrassmann space Projective space Spine space Coplanarity
Mathematics Subject Classification51A15 51A45
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