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A Bundle Representation for Continuous Geometries
1997
Advances in Applied Mathematics
We show that a reducible continuous geometry can be represented as the continuous sections of a bundle of irreducible continuous geometries. We relate this bundle representation to the Pierce sheaf of the continuous geometry and to the subdirect product representation Ä 4 Ž . the family of dimension functions D : J g Y and in fact D arJ s J J Ž .Ž . w x D a J l Z 5, Hilfsatz 3.3, p. 124 . In particular, we shall need the fact that each D is a positive modular valuation on LrJ, so it induces a
doi:10.1006/aama.1997.0548
fatcat:o3gqgb762bhqzk5tdahldwvbcu