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Open AccessArticle

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

1
Division of Applied Mathematics, Nanoscale Science and Technology Institute, Wonkwang University, Iksan 54538, Korea
2
Department of Applied Mathematics, Wonkwang University, 460, Iksan-daero, Iksan-Si, Jeonbuk 54538, Korea
3
School of Mathematics, Shandong University of Technology, Zibo 255049, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 482; https://doi.org/10.3390/math8040482
Received: 18 February 2020 / Revised: 22 March 2020 / Accepted: 27 March 2020 / Published: 1 April 2020
(This article belongs to the Special Issue Fuzziness and Mathematical Logic )
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 ) ]. View Full-Text
Keywords: cubic H-relational space; cubic H-reflexive relation; topological category; cartesian closed category; topological universe cubic H-relational space; cubic H-reflexive relation; topological category; cartesian closed category; topological universe
MDPI and ACS Style

Lee, J.-G.; Hur, K.; Chen, X. A Study on Cubic H-Relations in a Topological Universe Viewpoint. Mathematics 2020, 8, 482.

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