Quasi-Uniformity on BL-algebras

Authors

  • Rajab Ali Borzooei Department of Mathematics, Shahid Beheshti University, Tehran, Iran
  • Nader Kouhestani Department of Mathematics, Sistan and Balouchestan University, Zahedan, Ira

DOI:

https://doi.org/10.23755/rm.v35i0.423

Keywords:

BL-algebra, (semi)topological BL-algebra, filter, Quasi-uniforme space, Bicompletion

Abstract

See the pdf. file

References

A. Arhangel’skii, M. Tkachenko, Topological groups and related structures, Atlantis press, 2008.

R. A. Borzooei, G. R. Rezaei, N. Kouhestani, On (semi)topological BL-algebra, Iranian Journal of Mathematical Sciences and Informatics 6(1)

(2011), 59-77.

R. A. Borzooei, G. R. Rezaei, N. Kouhestani, Metrizability on (semi)topological BL-algebra, Soft Computing, 16 (2012), 1681-1690.

R. A. Borzooei, G. R. Rezaei, N. Kouhestani, Separation axioms in (semi)topological quotient BL-algebras, Soft Computing, 16 (2012), 1219-1227.

N. Bourbaki, Elements of mathematics general topology, Addison-Wesley Publishing Company, 1966.

D. Busneag, D. Piciu, Boolean BL-algebra of fractions, Annals of University of Craiova, Math. Comp. Soi. Ser., 31 (2004), 1-19.

L. C. Ciungu, Convergences in Perfect BL-algebras, Mathware Soft Computing, 14 (2007) 67-80.

J. Chvalina, B. Smetana, Algebraic Spaces and Set Decompositions, Ratio Mathematica, 34 (2018), 67-76.

A. Dinola, L. Leustean,Compact Representations of BL-algebra, Arch. Math. Logic, 42 (2003), 737-761.

P. Fletcher, W.F.Lindgren, Quasi-uniform Spaces, Lecture Notes in Pure and Applied Mathematics, Marcel dekker, New York, 77, 1982.

P. Hájek, Metamathematics of Fuzzy Logic, Kluwer academic publishers, 1998.

M. Haveshki, A. Borumand Saeid, E. Eslami, Some Types of Filters in BL-algebras, Soft computing, 10 (2006), 657-664.

M. Haveshki, E. Eslami and A. Borumand Saeid, A topology induced by uniformity on BL-algebras, Mathematical logic Quarterly, 53(2) (2007), 162-169.

S. Hoskova-Mayerova, An Overview of Topological and Fuzzy Topological Hypergroupoids, Ratio Mathematica, 33 (2017), 21-38.

T. Husain, Introduction to topological groups, W. B. Sunders Company, 1966.

H.P.A. Künzi, Quasi-uniform spaces-eleven years later, Top. Proc. 18, (1993), 143-171.

H.P.A. Künzi, J.Marin, S.Romaguera, Quasi-Uniformities on Topological semigroups and Bicompletion, Semigroups Forum, 62 (2001), 403-422.

H.P.A. Künzi, S. Romaguera, O. Sipacheva, The Doitchinov completion of a regular paratopological group, Serdica math. J., 24 (1998), 73-88.

J. Marin, S. Romaguera, Bicompleting the left quasi-uniformity of a paratopological group, Archiv Math. (Basel), 70 (1998), 104-110.

D. Marxen, Uniform semigroups, Math. Ann., 202 (1973), 27-36.

J. Mi Ko, Y. C. Kim, Closure operators on BL-algebras, Commun. Korean Math. Soc., 19(2) (2004), 219-232.

M.G. Murdeshwar, S.A. Naimpally, Quasi-Uniform Topological Spaces, 1966

A. Rezaei, A. Borumand Saeid, R. A. Borzooei, Relation between Hilbert Algebras and BE-Algebras, Applications and Applied Mathematics, 8(2) (2013), 573 - 584.

A. Weil, sur les espaces a structure uniforme et sur la topologiebgeneral, Gauthier-Villars, Paris, 1973.

Downloads

Published

2018-12-31

Issue

Vol. 35 (2018)

Section

Volume 35-2018

License

This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge. The journal is committed to real and immediate open access for academic work. All of the journal articles are free to access immediately from the date of publication. There are no charge for readers to download articles and reviews for their own scholarly use. Benefits of open access for authors, include:

  • Free access for all users worldwide
  • Increased visibility and readership
  • Rapid publication
  • No spatial constraints
  • Authors can share their research papers on their personal web-pages (i.e. ResearchGate, etc.)

Ratio Mathematica publishes open access articles under the terms of the Creative Commons Attribution (CC BY) License. The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed. Copyright on any research article published by Ratio Mathematica is retained by the author(s). Authors grant Ratio Mathematica a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified. 
For further information visit: https://creativecommons.org/licenses/by/3.0/. The following logo will appear in any paper that will be published from the volume number 31/2016 onwards.