# The erdös-dushnik-miller theorem for topological graphs and orders

@article{Milner1985TheET, title={The erd{\"o}s-dushnik-miller theorem for topological graphs and orders}, author={E. C. Milner and M. Pouzet}, journal={Order}, year={1985}, volume={1}, pages={249-257} }

A topological graph is a graph G=(V, E) on a topological space V such that the edge set E is a closed subset of the product space V x V. If the graph contains no infinite independent set then, by a well-known theorem of Erdös, Dushnik and Miller, for any infinite set L⊑V, there is a subset L′⊑L of the same oardinality |L′| = |L| such that the restriction G ↾ L′ is a complete graph. We investigate the question of whether the same conclusion holds if we weaken the hypothesis and assume only that… Expand

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