Affiliations: Department of Mathematics, Gangneung-Wonju National University, Gangneung, Gangwondo, Korea
Correspondence:
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Corresponding author. Yong Chan Kim, Department of Mathematics, Gangneung-Wonju National University, Gangneung, Gangwondo, E-mail: Korea.yck@gwnu.ac.kr.
Note: [1] This work was supported by Gangneung-Wonju National University.
Abstract: In this paper, we prove the existences of initial upper M-approximate operators and initial M-closed sets in commutative cl-monoids with order reverse involutions. From this fact, we define subspaces and product spaces for upper M-approximate operators and M-closed sets. Moreover, we investigate the relations between initial upper M-approximate operators and initial M-closed sets. We give their examples.
