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Embedding partially ordered spaces in topological semilattices

1972
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Proceedings of the American Mathematical Society
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A partial order F on a compact space S is called continuous if T is a closed subset of S x S. In this paper, we define and study an embedding of the arbitrary compact continuously partially ordered space (S, T) into a corresponding compact topological semilattice Sr-We show that the structure of entirely determines the structure of (S, T). We prove that the inverse images under O of components in Sr are the order components of (5, T), where elements a and b of 5 are defined to be in the same

doi:10.1090/s0002-9939-1972-0292724-7
fatcat:gwngztsexbhl5ojjffnd4gepsy