A METRIC-LIKE TOPOLOGY ON BL-ALGEBRAS | ||
| Journal of Algebraic Systems | ||
| دوره 9، شماره 2، فروردین 2022، صفحه 281-298 اصل مقاله (183.56 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2021.10296.1509 | ||
| نویسنده | ||
| Seyed M. A. Khatami* | ||
| Department of Computer Science, Birjand University of Technology, Birjand, Iran. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| BL-algebra؛ dual of BL-algebra؛ topological BL-algebra | ||
| مراجع | ||
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