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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Adamek J, Herrlich H, Strecker G (1990) Abstract and concrete categories. Wiley, New York
Arbib MA, Manes EG (1975) Arrows, structures, and functors: the categorical imperative. Academic Press, New York
Chang CL (1968) Fuzzy topological spaces. J Math Anal Appl 24:182–190
Giuli E (2005) On separated affine sets and epimorphisms. Topol Proc 29:509–519
Giuli E, Hofmann D (2009) Affine sets: the structure of complete objects and duality. Topol Appl 156:2129–2136
Lowen R (1976) Fuzzy topological spaces and fuzzy compactness. J Math Anal Appl 56:621–633
Lowen R, Srivastava AK (1989) \( {FTS}_{0}\): the epireflective hull of the Sierpinski object in FTS. Fuzzy Sets Syst 29:171–176
Manes EG (1976) Algebraic theories. Springer, New York
Singh SK, Srivastava AK (2013) A characterization of the category Q-TOP. Fuzzy Sets Syst 227:46–50
Solovyov SA (2008) Sobriety and spatiality in varieties of algebras. Fuzzy Sets Syst 159:2567–2585
Srivastava AK (1984) Fuzzy Sierpinski space. J Math Anal Appl 103:103–105
Srivastava AK, Srivastava R (1985) Fuzzy Sierpinski space: another note. J Fuzzy Math 3:99–103
Srivastava R, Srivastava AK, Choubey A (1994) Fuzzy closure spaces. J Fuzzy Math 2:525–534
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.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
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.
Additional information
Communicated by A. Di Nola.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Tiwari, H., Srivastava, R. A characterization of the category FCS. Soft Comput 23, 13001–13005 (2019). https://doi.org/10.1007/s00500-019-04270-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-019-04270-2