IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i7p1143-d785949.html
   My bibliography  Save this article

Algebraic Representation of Topologies on a Finite Set

Author

Listed:
  • Hongfeng Guo

    (School of Statistics and Mathematics, Shandong University of Finance and Economics, Jinan 250014, China)

  • Bing Xing

    (School of Statistics and Mathematics, Shandong University of Finance and Economics, Jinan 250014, China)

  • Ziwei Ming

    (School of Statistics and Mathematics, Shandong University of Finance and Economics, Jinan 250014, China)

  • Jun-E Feng

    (School of Mathematics, Shandong University, Jinan 250100, China)

Abstract

Since the 1930s, topological counting on finite sets has been an interesting work so as to enumerate the number of corresponding order relations on the sets. Starting from the semi-tensor product (STP), we give the expression of the relationship between subsets of finite sets from the perspective of algebra. Firstly, using the STP of matrices, we present the algebraic representation of the subset and complement of finite sets and corresponding structure matrices. Then, we investigate respectively the relationship between the intersection and union and intersection and minus of structure matrices. Finally, we provide an algorithm to enumerate the numbers of topologies on a finite set based on the above theorems.

Suggested Citation

  • Hongfeng Guo & Bing Xing & Ziwei Ming & Jun-E Feng, 2022. "Algebraic Representation of Topologies on a Finite Set," Mathematics, MDPI, vol. 10(7), pages 1-11, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1143-:d:785949
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/7/1143/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/7/1143/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Wen Liu & Shihua Fu & Jianli Zhao, 2021. "Set Stability and Set Stabilization of Boolean Control Networks Avoiding Undesirable Set," Mathematics, MDPI, vol. 9(22), pages 1-20, November.
    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. Qilong Sun & Haitao Li, 2022. "Robust Stabilization of Impulsive Boolean Control Networks with Function Perturbation," Mathematics, MDPI, vol. 10(21), pages 1-12, October.
    2. Du, Leihao & Zhang, Zhipeng & Xia, Chengyi, 2023. "A state-flipped approach to complete synchronization of Boolean networks," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    3. Wang, Jianjun & Liu, Wen & Fu, Shihua & Xia, Jianwei, 2022. "On robust set stability and set stabilization of probabilistic Boolean control networks," Applied Mathematics and Computation, Elsevier, vol. 422(C).

    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:10:y:2022:i:7:p:1143-:d:785949. 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.