A topology related to implication and upsets on a bounded BCK-algebra
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 topo...
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| Format: | Article |
| Language: | English |
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De Gruyter
2025-04-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2025-0133 |
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| author | Wu Supeng Liu Hui Yang Jiang |
| author_facet | Wu Supeng Liu Hui Yang Jiang |
| author_sort | Wu Supeng |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-4ce2f3e16ff94e4aa1249dad0d61d436 |
| institution | Kabale University |
| issn | 2391-5455 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj-art-4ce2f3e16ff94e4aa1249dad0d61d4362025-08-20T03:53:41ZengDe GruyterOpen Mathematics2391-54552025-04-01231262910.1515/math-2025-0133A topology related to implication and upsets on a bounded BCK-algebraWu Supeng0Liu Hui1Yang Jiang2School of Mathematics and Data Science, Shaanxi University of Science and Technology, Xi’an 710021, P. R. ChinaSchool of Mathematics and Data Science, Shaanxi University of Science and Technology, Xi’an 710021, P. R. ChinaSchool of Mathematics, Northwest University, Xian, 710127, P. R. ChinaThe 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.https://doi.org/10.1515/math-2025-0133bounded bck-algebraupsetsemitopological algebra03g2522a26 |
| spellingShingle | Wu Supeng Liu Hui Yang Jiang A topology related to implication and upsets on a bounded BCK-algebra Open Mathematics bounded bck-algebra upset semitopological algebra 03g25 22a26 |
| title | A topology related to implication and upsets on a bounded BCK-algebra |
| title_full | A topology related to implication and upsets on a bounded BCK-algebra |
| title_fullStr | A topology related to implication and upsets on a bounded BCK-algebra |
| title_full_unstemmed | A topology related to implication and upsets on a bounded BCK-algebra |
| title_short | A topology related to implication and upsets on a bounded BCK-algebra |
| title_sort | topology related to implication and upsets on a bounded bck algebra |
| topic | bounded bck-algebra upset semitopological algebra 03g25 22a26 |
| url | https://doi.org/10.1515/math-2025-0133 |
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