Analyzing Some Structural Properties of Topological B-Algebras
In this study, we investigate the topology on B-algebras: an algebraic system of propositional logic. We define here the notion of topological B-algebras (briefly, TB-algebras) and some properties are investigated. A characterization of TB-algebras based on neighborhoods is provided. We also provide...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2019/8683965 |
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| _version_ | 1832564810087137280 |
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| author | Narciso C. Gonzaga |
| author_facet | Narciso C. Gonzaga |
| author_sort | Narciso C. Gonzaga |
| collection | DOAJ |
| description | In this study, we investigate the topology on B-algebras: an algebraic system of propositional logic. We define here the notion of topological B-algebras (briefly, TB-algebras) and some properties are investigated. A characterization of TB-algebras based on neighborhoods is provided. We also provide a filterbase that generates a unique B-topology, making a TB-algebra in which the filterbase is a neighborhood base of the constant element, provided that the given B-algebra is commutative. Finally, we investigate subalgebras of TB-algebras and introduce the notion of quotient TB-algebras of the given B-algebra. |
| format | Article |
| id | doaj-art-256f53efe8c34e6ebddb7facf2187dda |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-256f53efe8c34e6ebddb7facf2187dda2025-02-03T01:10:09ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252019-01-01201910.1155/2019/86839658683965Analyzing Some Structural Properties of Topological B-AlgebrasNarciso C. Gonzaga0Mathematics Department, Bukidnon State University, Malaybalay City 8700, PhilippinesIn this study, we investigate the topology on B-algebras: an algebraic system of propositional logic. We define here the notion of topological B-algebras (briefly, TB-algebras) and some properties are investigated. A characterization of TB-algebras based on neighborhoods is provided. We also provide a filterbase that generates a unique B-topology, making a TB-algebra in which the filterbase is a neighborhood base of the constant element, provided that the given B-algebra is commutative. Finally, we investigate subalgebras of TB-algebras and introduce the notion of quotient TB-algebras of the given B-algebra.http://dx.doi.org/10.1155/2019/8683965 |
| spellingShingle | Narciso C. Gonzaga Analyzing Some Structural Properties of Topological B-Algebras International Journal of Mathematics and Mathematical Sciences |
| title | Analyzing Some Structural Properties of Topological B-Algebras |
| title_full | Analyzing Some Structural Properties of Topological B-Algebras |
| title_fullStr | Analyzing Some Structural Properties of Topological B-Algebras |
| title_full_unstemmed | Analyzing Some Structural Properties of Topological B-Algebras |
| title_short | Analyzing Some Structural Properties of Topological B-Algebras |
| title_sort | analyzing some structural properties of topological b algebras |
| url | http://dx.doi.org/10.1155/2019/8683965 |
| work_keys_str_mv | AT narcisocgonzaga analyzingsomestructuralpropertiesoftopologicalbalgebras |