IDEAS home Printed from https://ideas.repec.org/a/wsi/nmncxx/v15y2019i01ns1793005719500017.html
   My bibliography  Save this article

Quantale-Valued Generalizations of Approach Groups

Author

Listed:
  • T. M. G. Ahsanullah

    (Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia)

  • Gunther Jäger

    (School of Mechanical Engineering, University of Applied Sciences Stralsund, 18435 Stralsund, Germany)

Abstract

The motive behind this paper is to generalize the concept of approach groups. In so doing, we introduce various categories, specifically, the categories of quantale-valued convergence groups, quantale-valued approach groups, quantale-valued gauge groups and quantale-valued approach system groups, and study their functorial relationships including the fact that the category of quantale-valued gauge groups as well as the category of quantale-valued approach system groups is topological over the category of groups. Besides obtaining a variety of categorical connections, we note that if the quantale is linearly ordered satisfying certain conditions, then the categories of quantale-valued approach system groups and quantale-valued gauge groups are isomorphic. Finally, we look into the embeddings of the category of quantale-valued metric groups into the categories of quantale-valued generalizations of approach groups including commutativity of some diagrams.

Suggested Citation

  • T. M. G. Ahsanullah & Gunther Jäger, 2019. "Quantale-Valued Generalizations of Approach Groups," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-30, March.
    • Handle: RePEc:wsi:nmncxx:v:15:y:2019:i:01:n:s1793005719500017
    DOI: 10.1142/S1793005719500017
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S1793005719500017
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S1793005719500017?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.

    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:wsi:nmncxx:v:15:y:2019:i:01:n:s1793005719500017. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/nmnc/nmnc.shtml .

    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.