Embedding convex geometries and a bound on convex dimension

2015/02/06 by Richter, Michael, Rogers, Luke G.
#52A01 #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1502.01941

Abstract

The notion of an abstract convex geometry offers an abstraction of the standard notion of convexity in a linear space. Kashiwabara, Nakamura and Okamoto introduce the notion of a generalized convex shelling into ℝ and prove that a convex geometry may always be represented with such a shelling. We provide a new, shorter proof of their result using a recent representation theorem of Richter and Rubinstein, and deduce a different upper bound on the dimension of the shelling.

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