Convex Geometries

K. Adaricheva and J. B. Nation
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K. Adaricheva: Nazarbayev University, School of Science and Technology
J. B. Nation: University of Hawaii, Department of Mathematics

Chapter Chapter 5 in Lattice Theory: Special Topics and Applications, 2016, pp 153-179 from Springer

Abstract: Abstract The origin of convex geometries lies in combinatorics, and the goal of the study of finite convex geometries was to develop the combinatorial abstraction of convexity. Similarly, the theory of matroids is a combinatorial abstraction of independent sets; see the survey of B. Dietrich [125]. Since both abstractions can be formulated in the framework of a closure operator on a finite set, one can associate with a convex geometry or a matroid the closure lattice of the corresponding closure operator. This also becomes the foundation for the generalization of these concepts to the infinite case.

Keywords: Closure System; Closure Operator; Complete Lattice; Closure Space; Generalize Convex (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-44236-5_5

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