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A Study on Cubic H -Relations in a Topological Universe Viewpoint

Author

Listed:
  • Jeong-Gon Lee

    (Division of Applied Mathematics, Nanoscale Science and Technology Institute, Wonkwang University, Iksan 54538, Korea)

  • Kul Hur

    (Department of Applied Mathematics, Wonkwang University, 460, Iksan-daero, Iksan-Si, Jeonbuk 54538, Korea)

  • Xueyou Chen

    (School of Mathematics, Shandong University of Technology, Zibo 255049, China)

Abstract

We introduce the concrete category CRel P ( H ) [resp. CRel R ( H ) ] of cubic H -relational spaces and P-preserving [resp. R-preserving] mappings between them and study it in a topological universe viewpoint. In addition, we prove that it is Cartesian closed over Set . Next, we introduce the subcategory CRel P , R ( H ) [resp. CRel R , R ( H ) ] of CRel P ( H ) [resp. CRel R ( H ) ] and investigate it in the sense of a topological universe. In particular, we obtain exponential objects in CRel P , R ( H ) [resp. CRel R , R ( H ) ] quite different from those in CRel P ( H ) [resp. CRel R ( H ) ].

Suggested Citation

  • Jeong-Gon Lee & Kul Hur & Xueyou Chen, 2020. "A Study on Cubic H -Relations in a Topological Universe Viewpoint," Mathematics, MDPI, vol. 8(4), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:482-:d:340029
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    References listed on IDEAS

    as
    1. Naveed Yaqoob & Nabilah Abughazalah, 2019. "Finite Switchboard State Machines Based on Cubic Sets," Complexity, Hindawi, vol. 2019, pages 1-13, July.
    2. Kul Hur & Su Youn Jang & Hee Won Kang, 2005. "Intuitionistic H -fuzzy relations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-12, January.
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