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Parallel axiom in convexity lattices. (English) Zbl 0768.06008

Author’s summary: The convexity lattices, introduced by Bennett and Birkhoff, generalize the lattices of convex sets. The authors present three forms of the Parallel Axiom in such lattices and define Euclidean and two classes of non-Euclidean lattices via the number of parallel lines through a point. The paper deals with these three classes of lattices.
Reviewer: R.A.Alo (Houston)

MSC:

06B05 Structure theory of lattices
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