Closure and preferences

Christopher P. Chambers, Alan D. Miller, M. Bumin Yenmez

Research output: Contribution to journalArticlepeer-review


We investigate the results of Kreps (1979), dropping his completeness axiom. As an added generalization, we work on arbitrary lattices, rather than a lattice of sets. We show that one of the properties of Kreps is intimately tied with representation via a closure operator. That is, a preference satisfies Kreps’ axiom (and a few other mild conditions) if and only if there is a closure operator on the lattice, such that preferences over elements of the lattice coincide with dominance of their closures. We tie the work to recent literature by Richter and Rubinstein (2015).

Original languageEnglish
Pages (from-to)161-166
Number of pages6
JournalJournal of Mathematical Economics
StatePublished - May 2020

Bibliographical note

Publisher Copyright:
© 2020 Elsevier B.V.


  • Closure
  • Kreps
  • Menu

ASJC Scopus subject areas

  • Economics and Econometrics
  • Applied Mathematics


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