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Homogeneous Geometries
Author(s) -
Evans David M.
Publication year - 1986
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-52.2.305
Subject(s) - homogeneous , citation , mathematics , computer science , library science , combinatorics
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: