On Scattered Convex Geometries |
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| Authors: | Kira Adaricheva Maurice Pouzet |
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| Institution: | 1.Department of Mathematical Sciences,Yeshiva University,New York,USA;2.Department of Mathematics, School of Science and Technology,Nazarbayev University,Astana,Kazakhstan;3.Univ. Lyon, Université Claude-Bernard Lyon1, CNRS UMR 5208, Institut Camille Jordan,Villeurbanne,France;4.Mathematics & Statistics Department,University of Calgary,Calgary,Canada |
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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 Ω(η), 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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