A METRIC-LIKE TOPOLOGY ON BL-ALGEBRAS

Document Type : Original Manuscript

Author

Department of Computer Science, Birjand University of Technology, Birjand, Iran.

Abstract

This paper is devoted to introduce a topology on BL-algebras, makes them semitopological algebras. For any BL-algebra $\mathcal{L}=(L, \wedge, \vee, *, \too , 0, 1)$, the introduced topology is defined by a distance-like function between elements of $L$ which is defined by $a \leftrightarrow b=(a\too b)*(b\too a)$. We will show that when the continuous scale $[0,1]$ is endowed to be a BL-algebra, then this topology admits some of the most important properties of the metric topology. Finally, we will show that this topology can be examined by a similar topology on dual of BL-algebras as well.

Keywords

References

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Journal of Algebraic Systems
Volume 9, Issue 2
January 2022
Pages 281-298

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