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
• DOI: 10.1007/bf00160623

✦ 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.