A Half-Space Approach to Order Dimension
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- Foldes, S. & Szigeti, J. Order (2007) 24: 59. doi:10.1007/s11083-007-9059-z
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The aim of the present paper is to investigate the half-spaces in the convexity structure of all quasiorders on a given set and to use them in an alternative approach to classical order dimension. The main result states that linear orders can almost always be replaced by half-space quasiorders in the definition of the dimension of a partially ordered set.