Embedding of Topological Posets in Hyperspaces

Gerald Beer, Efe A. Ok

    Research output: Contribution to journalArticlepeer-review


    We study the problem of topologically order-embedding a given topological poset (X, ≤) in the space of all closed subsets of X which is topologized by the Fell topology and ordered by set inclusion. We show that this can be achieved whenever (X, ≤) is a topological semilattice (resp. lattice) or a topological po-group, and X is locally compact and order-connected (resp. connected). We give limiting examples to show that these results are tight, and provide several applications of them. In particular, a locally compact version of the Urysohn-Carruth metrization theorem is obtained, a new fixed point theorem of Tarski-Kantorovich type is proved, and it is found that every locally compact and connected Hausdorff topological lattice is a completely regular ordered space.

    Original languageEnglish (US)
    Pages (from-to)515-540
    Number of pages26
    JournalJournal of Convex Analysis
    Issue number2
    StatePublished - 2023


    • Fell topology
    • Topological poset
    • complete semilattice homomorphism
    • hyperspace
    • radially convex metric
    • topological order-embedding
    • topological po-group
    • topological semilattice

    ASJC Scopus subject areas

    • Analysis
    • General Mathematics


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