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Topological BCL+- Algebras

Received: 14 February 2014     Published: 20 March 2014
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Abstract

BCL/BCL+-algebras [1, 2] are more extensive class than BCK/BCI/BCH-algebras [5-8], introduced by Yonghong Liu. In this paper, we aim to embed topological structure in BCL+-algebras, thus we should be introduced to the notion of “good taste”, which is both topological space and metric space. Thereupon, some fundamental properties of topological BCL+-algebras are obtained.

Published in Pure and Applied Mathematics Journal (Volume 3, Issue 1)
DOI 10.11648/j.pamj.20140301.13
Page(s) 11-13
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

BCL-Algebra, BCL+-Algebra, Topological BCL+-Algebra

References
[1] Y. H. Liu, "A New Branch of the Pure Algebra: BCL-Algebras", Advances in Pure Mathematics, vol. 1, no. 5, pp. 297-299, 2011.
[2] Y. H. Liu, "On BCL+-Algebras", Advances in Pure Mathematics, vol. 2, no. 1, pp. 59-61, 2012.
[3] A. K. Deena and H. Rodyna, "On BCL-Algebra", Journal of Advances in Mathematics, vol. 3, no. 2, pp. 184-190, 2013.
[4] Y. H. Liu, "Partial Orders in BCL+-Algebra", Journal of Advances in Mathematics, vol. 5, no. 1, pp. 630-634, 2013.
[5] Y. Imai and K. Iséki, "On Axiom System of Propositional Cal-culi XIV," Proceedings of the Japan Academy, vol. 42, no. 1, pp. 19-22, 1966.
[6] K. Iséki, "An Algebra Related with a Propositional Calculus," Proceedings of the Japan Academy, vol. 42, no. 1, pp. 26-29, 1966.
[7] K. Iseki, "On BCI-Algebras," Mathematics Seminar Notes (Kobe University), vol. 8, no. 1, pp. 125-130, 1980.
[8] Q. P. Hu and X. Li, "On BCH-Algebras," Mathematics Seminar Notes (Kobe University), vol. 11, no. 2, pp. 313-320, 1983.
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    Yonghong Liu. (2014). Topological BCL+- Algebras. Pure and Applied Mathematics Journal, 3(1), 11-13. https://doi.org/10.11648/j.pamj.20140301.13

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    ACS Style

    Yonghong Liu. Topological BCL+- Algebras. Pure Appl. Math. J. 2014, 3(1), 11-13. doi: 10.11648/j.pamj.20140301.13

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    AMA Style

    Yonghong Liu. Topological BCL+- Algebras. Pure Appl Math J. 2014;3(1):11-13. doi: 10.11648/j.pamj.20140301.13

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  • @article{10.11648/j.pamj.20140301.13,
      author = {Yonghong Liu},
      title = {Topological BCL+- Algebras},
      journal = {Pure and Applied Mathematics Journal},
      volume = {3},
      number = {1},
      pages = {11-13},
      doi = {10.11648/j.pamj.20140301.13},
      url = {https://doi.org/10.11648/j.pamj.20140301.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20140301.13},
      abstract = {BCL/BCL+-algebras [1, 2] are more extensive class than BCK/BCI/BCH-algebras [5-8], introduced by Yonghong Liu. In this paper, we aim to embed topological structure in BCL+-algebras, thus we should be introduced to the notion of “good taste”, which is both topological space and metric space. Thereupon, some fundamental properties of topological BCL+-algebras are obtained.},
     year = {2014}
    }
    

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  • TY  - JOUR
    T1  - Topological BCL+- Algebras
    AU  - Yonghong Liu
    Y1  - 2014/03/20
    PY  - 2014
    N1  - https://doi.org/10.11648/j.pamj.20140301.13
    DO  - 10.11648/j.pamj.20140301.13
    T2  - Pure and Applied Mathematics Journal
    JF  - Pure and Applied Mathematics Journal
    JO  - Pure and Applied Mathematics Journal
    SP  - 11
    EP  - 13
    PB  - Science Publishing Group
    SN  - 2326-9812
    UR  - https://doi.org/10.11648/j.pamj.20140301.13
    AB  - BCL/BCL+-algebras [1, 2] are more extensive class than BCK/BCI/BCH-algebras [5-8], introduced by Yonghong Liu. In this paper, we aim to embed topological structure in BCL+-algebras, thus we should be introduced to the notion of “good taste”, which is both topological space and metric space. Thereupon, some fundamental properties of topological BCL+-algebras are obtained.
    VL  - 3
    IS  - 1
    ER  - 

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Author Information
  • School of Automation, Wuhan University of Technology, Wuhan, China

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