Abstract

Given a hyper BCK-algebra (H,*,0), we introduce some subsets of H and use them to generate two closure opeeatots on H. In this paper we show that each of tje two closurenoperators on H can be utilized to form a base for some topology on H.

Highlights

  • The study of BCK-algebras was initiated by Y

  • By using the sets LH (A) and RH (A), we introduce the bases BL(H) and BR(H) and the induced topologies τL(H) and τR(H) by these sets, respectively, and investigate their related properties [7, 8]

  • We present two closure operators on a hyper BCK-algebra and consider the respective topologies they generate

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Summary

Introduction

The study of BCK-algebras was initiated by Y. Iseki [4] in 1966 as a generalization of the concept of set theoretic difference and propositional calculi. The hyperstructure theory (or multialgebras) was introduced in 1934 by F. In [5], Y.B. Jun et al applied the hyperstructures to BCK-algebras and introduced the notion of a hyper BCK-algebra which is a generalization of a BCK-algebra. By using the sets LH (A) and RH (A), we introduce the bases BL(H) and BR(H) and the induced topologies τL(H) and τR(H) by these sets, respectively, and investigate their related properties [7, 8]. We present two closure operators on a hyper BCK-algebra and consider the respective topologies they generate. It is shown that these topologies coincide, respectively, with the topologies generated by BL(H) and BR(H)

Preliminaries
Known Results
Topology Induced by RHLH
Topology Induced by LHRH
Conclusion
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