IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v134y2025icp31-41.html
   My bibliography  Save this article

Upper semicontinuous utilities for all upper semicontinuous total preorders

Author

Listed:
  • Bosi, Gianni
  • Sbaiz, Gabriele

Abstract

Let X be an arbitrary nonempty set. Then a topology t on X is said to be completely useful (or upper useful) if every upper semicontinuous total preorder ≾ on the topological space (X,t) can be represented by an upper semicontinuous real-valued order-preserving function (i.e., utility function). In this paper the structures of completely useful topologies on X will be deeply studied and clarified. In particular, completely useful topologies will be characterized through the new notions of super-short and strongly separable topologies. Further, the incorporation of the Souslin Hypothesis and the relevance of these characterizations in mathematical utility theory will be discussed. Finally, various interrelations between the concepts of complete usefulness and other topological concepts that are of interest not only in mathematical utility theory are analyzed.

Suggested Citation

  • Bosi, Gianni & Sbaiz, Gabriele, 2025. "Upper semicontinuous utilities for all upper semicontinuous total preorders," Mathematical Social Sciences, Elsevier, vol. 134(C), pages 31-41.
    • Handle: RePEc:eee:matsoc:v:134:y:2025:i:c:p:31-41
    DOI: 10.1016/j.mathsocsci.2025.01.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165489625000101
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.mathsocsci.2025.01.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    More about this item

    Keywords

    Super-short topology; Strongly separable topology; Isolated set; Lindelöf topology;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matsoc:v:134:y:2025:i:c:p:31-41. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.