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Ordered Sets and Order Homomorphisms 1
Order Homomorphisms in Euclidean Space
A Miscellany of Representations
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Arrow-Hahn assume binary relation choose closed convergence closed subsets completes the proof continuous function continuous isotone function continuous order isomorphism continuous total preorder continuous utility function contradiction countable set Debreu Debreu order separability define Definition disjoint Economic Theory element equivalent euclidean exists a continuous exists a real-valued follows function f Hence Herden implies interval order irreflexive isotone Jaffray Journal of Mathematical Kannai locally nonsatiated lower semicontinuous manifold mapping Mathematical Economics Mehta Nachbin's Neuefeind nonempty normally preordered open sets open subset order dense subset order topology ordered set pair preference relations preordered set preordered topological space Proposition rational numbers real number real-valued function real-valued order isomorphism representation respectively second countable strict partial order strict weak order strongly pseudotransitive Suppose topological space topology of closed transitive upper semicontinuous vector whence x y y x y z y y x