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The dimension theorem in axiomatic geometry

✍ Scribed by Claude-Alain Faure; Alfred Frölicher


Publisher
Springer
Year
1996
Tongue
English
Weight
659 KB
Volume
60
Category
Article
ISSN
0046-5755

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✦ Synopsis


Given a matroid and an integer n _> 0, eleven conditions are shown to be equivalent to the validity of the rank formula r(E V F) + r(E A F) = r(E) + r(F) for subspaces satisfying r(E A F) > n. For n = 0 one finds the projective geometries. The case n = 1 also includes the affine and the hyperbolic geometries, the case n = 2 the Mtbius geometries. The general case covers the incidence geometries of grade n of Wille.


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