Extreme point axioms for closure spaces

DOI10.1016/j.disc.2006.04.034zbMath1110.54001OpenAlexW1990826684MaRDI QIDQ856869

Kazutoshi Ando

Publication date: 14 December 2006

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2006.04.034

zbMATH Keywords

closure operatorchoice functionantimatroidmatroidconvex geometryAizerman conditionChernoff conditionexchange conditionexpansion conditionextreme point operatorMinkowski-Krein-Milman condition

Mathematics Subject Classification ID

Axiomatic and generalized convexity (52A01) Topological spaces and generalizations (closure spaces, etc.) (54A05) Combinatorial aspects of matroids and geometric lattices (05B35) Individual preferences (91B08)

Related Items (10)

Essentiality and convexity in the ranking of opportunity sets ⋮ Orders on subsets rationalised by abstract convex geometries ⋮ Resolutions of convex geometries ⋮ Matroids on convex geometries (cg-matroids) ⋮ An envelope operator for full convexity to define polyhedral models in digital spaces ⋮ Full convexity for polyhedral models in digital spaces ⋮ Matroids on convex geometries: subclasses, operations, and optimization ⋮ Local topology of the free complex of a two-dimensional generalized convex shelling ⋮ Characterizations of the convex geometries arising from the double shellings of posets ⋮ Choice functions and extensive operators

Cites Work

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• Greedoids
• Choice functions over a finite set: A summary
• The theory of convex geometries
• Choice functions and abstract convex geometries
• Closure lattices
• General theory of best variants choice: Some aspects
• The duality between the anti-exchange closure operators and the path independent choice operators on a finite set

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