On scattered convex geometries
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Date
2015
Authors
Adaricheva, Kira
Pouzet, Maurice
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Abstract
A convex geometry is a closure space satisfying the anti-exchange axiom. For several
types of algebraic convex geometries we describe when the collection of closed sets is order scattered, in terms of obstructions to the semilattice of compact elements. In particular, a semilattice ( ), that does not appear among minimal obstructions to order-scattered algebraic modular lattices, plays a prominent role in convex geometries case. The connection to topological scatteredness is established in convex geometries of relatively convex sets
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Keywords
Research Subject Categories::MATHEMATICS, convex geometries
Citation
Adaricheva Kira, Pouzet Maurice; 2015; On scattered convex geometries; arXiv.org