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Soft Computing

, Volume 23, Issue 24, pp 13001–13005 | Cite as

A characterization of the category FCS

  • Harshita TiwariEmail author
  • Rekha Srivastava
Foundations
  • 85 Downloads

Abstract

Srivastava et al. (J Fuzzy Math 2:525–534, 1994) introduced the notion of a fuzzy closure space and studied the category FCS of fuzzy closure spaces and fuzzy closure preserving maps. In this article, we have introduced the Sierpinski fuzzy closure space and proved that it is a Sierpinski object in the category FCS. Further, a characterization (up to an isomorphism) of the category FCS is given, with the help of the Sierpinski fuzzy closure space.

Keywords

Fuzzy closure space Sierpinski fuzzy closure space Sierpinski object 

Notes

Acknowledgements

The first author Harshita Tiwari gratefully acknowledges the financial support in the form of INSPIRE fellowship (offer letter no. DST/INSPIRE Fellowship/2017/IF170407), given by the Department of Science and Technology, New Delhi.

Compliance with ethical standards

Conflict of interest

Rekha Srivastava has no conflict of interest.

Human and animal rights

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

References

  1. Adamek J, Herrlich H, Strecker G (1990) Abstract and concrete categories. Wiley, New YorkzbMATHGoogle Scholar
  2. Arbib MA, Manes EG (1975) Arrows, structures, and functors: the categorical imperative. Academic Press, New YorkzbMATHGoogle Scholar
  3. Chang CL (1968) Fuzzy topological spaces. J Math Anal Appl 24:182–190MathSciNetCrossRefGoogle Scholar
  4. Giuli E (2005) On separated affine sets and epimorphisms. Topol Proc 29:509–519MathSciNetzbMATHGoogle Scholar
  5. Giuli E, Hofmann D (2009) Affine sets: the structure of complete objects and duality. Topol Appl 156:2129–2136MathSciNetCrossRefGoogle Scholar
  6. Lowen R (1976) Fuzzy topological spaces and fuzzy compactness. J Math Anal Appl 56:621–633MathSciNetCrossRefGoogle Scholar
  7. Lowen R, Srivastava AK (1989) \( {FTS}_{0}\): the epireflective hull of the Sierpinski object in FTS. Fuzzy Sets Syst 29:171–176CrossRefGoogle Scholar
  8. Manes EG (1976) Algebraic theories. Springer, New YorkCrossRefGoogle Scholar
  9. Singh SK, Srivastava AK (2013) A characterization of the category Q-TOP. Fuzzy Sets Syst 227:46–50MathSciNetCrossRefGoogle Scholar
  10. Solovyov SA (2008) Sobriety and spatiality in varieties of algebras. Fuzzy Sets Syst 159:2567–2585MathSciNetCrossRefGoogle Scholar
  11. Srivastava AK (1984) Fuzzy Sierpinski space. J Math Anal Appl 103:103–105MathSciNetCrossRefGoogle Scholar
  12. Srivastava AK, Srivastava R (1985) Fuzzy Sierpinski space: another note. J Fuzzy Math 3:99–103MathSciNetzbMATHGoogle Scholar
  13. Srivastava R, Srivastava AK, Choubey A (1994) Fuzzy closure spaces. J Fuzzy Math 2:525–534MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesIndian Institute of Technology (Banaras Hindu University)VaranasiIndia

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