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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Dimension de krull des ensembles ordonnes

References

SHOWING 1-7 OF 7 REFERENCES
Monotone subnets in partially ordered sets
A Partition Calculus in Set Theory
Complete ordered sets with no infinite antichains
Well quasi-ordered sets and ideals in free semigroups and algebras
Topology and order
Partial well-ordering of sets of vectors
Partially Ordered Sets