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Semicontinuous planar total preorders on non-separable metric spaces
María Jesús Campión,Juan Carlos Candeal,Esteban Induráin 대한수학회 2009 대한수학회지 Vol.46 No.4
We prove that every non-separable connected metric space can be endowed with a total preorder that is order-isomorphic to a non-representable subset of the lexicographic plane and semicontinuous with respect to the metric topology. We prove that every non-separable connected metric space can be endowed with a total preorder that is order-isomorphic to a non-representable subset of the lexicographic plane and semicontinuous with respect to the metric topology.