Homogeneous Geometries
نویسنده
چکیده
For the purposes of this paper, a geometry will consist of a set together with a closure operation on that set, satisfying the exchange condition, and under which singletons are closed (for more precise definitions, see §2.1). The geometry is homogeneous if in the automorphism group of the geometry, the pointwise stabilizer of any finitedimensional closed subset of the geometry is transitive on the complement of the subset. The geometry is degenerate if any subset is closed and is locally finite if the closure of a finite subset is finite. We aim to provide an elementary proof of the following:
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