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Uniform BL-algebras

  • R. Khanegir
  • G. R. Rezaei
  • N. Kouhestani
Foundations
  • 28 Downloads

Abstract

In this paper, we define the notion of uniform BL-algebras and derive some conditions under which the operations of BL-algebras are uniformly continuous. Also, some properties of uniform topology are discussed. Finally, we use some types of congruence relations to construct some uniformities and analyze the relationship between these uniformities.

Keywords

BL-algebra Ideal Filter Uniform BL-algebra Uniform topology 

Notes

Acknowledgements

The authors would like to express their sincere thanks to the referees for their valuable suggestions and comments.

Compliance with ethical standards

Conflict of interest

Authors declare that they have not conflict of interest.

Human and animal rights

This article does not contain any studies with human participants performed by any of the authors. This article does not contain any studies with animals performed by any of the authors.

References

  1. Arhangel’skii A, Tkachenko M (2008) Topological groups and related structures. Atlantis Press, AmsterdamCrossRefGoogle Scholar
  2. Barbieri G Weber H (1998) A topological approach to the study of fuzzy measures. In: Functional analysis and economic theory (Samos, 1996). Springer, Berlin, pp 17–46CrossRefGoogle Scholar
  3. Borzooei RA, Rezaei GR, Kouhestani N (2011) On (semi)topological BL-algebras. Iran J Math Sci Inform 6(1):59–77MathSciNetzbMATHGoogle Scholar
  4. Borzooei RA, Rezaei GR, Kouhestani N (2012a) Metrizability on (semi)topological BL-algebras. Soft Comput 16:1681–1690CrossRefGoogle Scholar
  5. Borzooei RA, Rezaei GR, Kouhestani N (2012b) Separation axioms in (semi)topological quotient BL-algebras. Soft Comput 16:1219–1227CrossRefGoogle Scholar
  6. Bourbaki N (1948) Topologie generale. ParisGoogle Scholar
  7. Engelking R (1989) General topology. Heldermann, BerlinzbMATHGoogle Scholar
  8. Eslami E, Haghani FK (2009) Pure filters and stable topology on \(BL\)-algebras. Kybernetika 45(3):491–506MathSciNetzbMATHGoogle Scholar
  9. Graziano MG (2000) Uniformities of Fréchet-Nikodym type on Vitali spaces. Semigroup Forum 61(1):91–115MathSciNetCrossRefGoogle Scholar
  10. Hájek P (1998) Metamathematics of fuzzy logic. Kluwer Academic Publishers, DordrechtCrossRefGoogle Scholar
  11. Haveshki M, Eslami E, Borumand Saeid A (2007) A topology induced by uniformity on BL-algebras. Math Log Q 53(2):162–169MathSciNetCrossRefGoogle Scholar
  12. Husain T (1966) Introduction to topological groups. W. B. Sunders Company, PhiladelphiazbMATHGoogle Scholar
  13. Joshi KD (1997) Introduction to general topology. New Age International Publisher, New DelhiGoogle Scholar
  14. Lele C, Nganou JB (2013) MV-algebras derived from ideals in BL-algebras. Fuzzy Sets Syst 218:103–113MathSciNetCrossRefGoogle Scholar
  15. Roelcke W, Dierolf S (1981) Uniform structures on topological groups and their quotients. McGraw-Hill International Book Co., New York, Advanced Book ProgramGoogle Scholar
  16. Weber H (1991) Uniform lattices. I: a generalization of topological Riesz spaces and topological Boolean rings. Annali di Mtematica Pura e Applicata (4) 160:347–370MathSciNetCrossRefGoogle Scholar
  17. Weber H (1993) Uniform lattices. II: order continuity and exhaustivity. Annali di Matematica Pura e Applicata (4) 165:133–158MathSciNetCrossRefGoogle Scholar
  18. Weil A (1938) Sur les espaces à structure uniforme et sur la topologie générale. ParisGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Sistan and BaluchestanZahedanIran
  2. 2.Fuzzy Systems Research CenterUniversity of Sistan and BaluchestanZahedanIran

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