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|Paper IPM / M / 8980||
In this paper we prove that any T1 subspace of a continuous dcpo with the relative Scott topology can be "modeled" by a continuous poset. Using this result we are able to show that any T1 topological space (X, τ) is homeomorphic to the space of maximal elements of a continuous poset. We also find a bitopological characterization of a topological space (X, τ) that can modeled by a continuous poset. It is proved that for any T1 topological space (X, τ) there is a T1 topology T* on X such that (X, τ, τ*) is pairwise completely regular.
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