IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i4p791-d1057607.html
   My bibliography  Save this article

Continuous Selections and Extremally Disconnected Spaces

Author

Listed:
  • Adolfo Pimienta

    (Facultad de Ciencias Básicas y Biomédicas, Universidad Simón Bolivar, Barranquilla 080002, Colombia)

  • Manuel Sanchis

    (Institut de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, 12071 Castelló, Spain)

Abstract

This paper deals with extremally disconnected spaces and extremally disconnected P -spaces. A space X is said to be extremally disconnected if, for every open subset V of X , the closure of V in X is also an open set. P -spaces are spaces in which the intersection of countably many open sets is an open set. The authors present a new characterization of extremally disconnected spaces, and the extremally disconnected P -spaces, by means of selection theory. If X is either an extremally disconnected space or an extremally disconnected P -space, then the usual theorems of extension of real-valued continuous functions for a dense subset S of X can be deduced from our results. A corollary of our outcomes is that every nondiscrete space X of nonmeasurable cardinality has a dense subset S such that S is not C -embedded in X .

Suggested Citation

  • Adolfo Pimienta & Manuel Sanchis, 2023. "Continuous Selections and Extremally Disconnected Spaces," Mathematics, MDPI, vol. 11(4), pages 1-8, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:791-:d:1057607
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/4/791/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/4/791/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. M. Ali Khan & Metin Uyanik, 2021. "The Yannelis–Prabhakar theorem on upper semi-continuous selections in paracompact spaces: extensions and applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 799-840, April.
    2. Luisa Di Piazza & Kazimierz Musiał, 2020. "Decompositions of Weakly Compact Valued Integrable Multifunctions," Mathematics, MDPI, vol. 8(6), pages 1-13, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Prokopovych, Pavlo & Yannelis, Nicholas C., 2023. "On monotone pure-strategy Bayesian-Nash equilibria of a generalized contest," Games and Economic Behavior, Elsevier, vol. 140(C), pages 348-362.
    2. Uyanik, Metin & Khan, M. Ali, 2022. "The continuity postulate in economic theory: A deconstruction and an integration," Journal of Mathematical Economics, Elsevier, vol. 101(C).
    3. Pavlo Prokopovych & Nicholas C. Yannelis, 2022. "On nondegenerate equilibria of double auctions with several buyers and a price floor," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 625-654, April.

    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:gam:jmathe:v:11:y:2023:i:4:p:791-:d:1057607. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.