Topological closure of translation invariant preorders

Efe A. Ok, Gil Riella

    Research output: Contribution to journalArticlepeer-review


    Our primary query is to find conditions under which the closure of a preorder on a topological space remains transitive. We study this problem for translation invariant preorders on topological groups. The results are fairly positive; we find that the closure of preorders and normal orders remain as such in this context. The same is true for factor orders as well under quite general conditions. In turn, in the context of topological linear spaces, these results allow us to obtain a simple condition under which the order-duals with respect to a vector order and its closure coincide. Various order-theoretic applications of these results are also provided in the paper.

    Original languageEnglish (US)
    Pages (from-to)737-745
    Number of pages9
    JournalMathematics of Operations Research
    Issue number3
    StatePublished - Aug 2014


    • Closure
    • Transitive closure
    • Translation invariance
    • Vector preorder

    ASJC Scopus subject areas

    • General Mathematics
    • Computer Science Applications
    • Management Science and Operations Research


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