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arXiv · 1909.03803

A metric-like topology yon BL-algebras

Seyed Mohammad Amin Khatami
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Abstract

This paper is devoted to introduce a topology on BL-algebras, makes them semitopological algebras. For any BL-algebra $\mathcal{L}=(L, \wedge, \vee, *, \to , 0, 1)$, the introduced topology is defined by a distance-like function between elements of $L$ which is defined by $a \leftrightarrow b=(a\to b)*(b\to a)$. 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.

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BibTeXRIS

Seyed Mohammad Amin Khatami. 2019-08-26. A metric-like topology yon BL-algebras. https://doi.org/10.22044/jas.2021.10296.1509

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