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

Jeong-Gon Lee, Kul Hur and Xueyou Chen
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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

Mathematics, 2020, vol. 8, issue 4, 1-18

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 ) ].

Keywords: cubic H -relational space; cubic H -reflexive relation; topological category; cartesian closed category; topological universe (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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