A topology related to implication and upsets on a bounded BCK-algebra - Wu Supeng; Liu Hui; Yang Jiang (Open Mathematics)
The main purpose of this article is to investigate a topology based on implication and upsets in a bounded BCK-algebra. First, we introduce a special kind of sets associated with implication and upsets in a bounded BCK-algebra, and some basic properties of these sets are derived. Furthermore, a topology related to implication and upsets is constructed by means of the sets. Moreover, we discuss some topological properties of the topology such as compactness and continuity. In particular, it is proved that a Glivenko BCK-algebra with the topology for implication is a left topological BCK-algebra. Also, a bounded product BCK-algebra with such topology for product is a para-topological BCK-algebra. Finally, the relationship between the topology and the quotient topology on a bounded quotient BCK-algebra is revealed.