Normality and Its Variants on Fuzzy Isotone Spaces

DOI: 10.4236/apm.2013.37084   PDF   HTML   XML   3,173 Downloads   4,977 Views  

Abstract

The study of fuzzy sets is specifically designed to mathematically represent uncertainty and vagueness by assigning values of membership to objects that belong to a particular set. This notion has been broadly extended to other areas of topology where various topological concepts have been shown to hold on fuzzy topology. Some notions naturally extend to closure spaces without requiring a lot of modification of the underlying topological ideas. This work investigates the variants of normality on fuzzy isotone spaces.

Share and Cite:

S. Gathigi, M. Gichuki, P. Otieno and H. Were, "Normality and Its Variants on Fuzzy Isotone Spaces," Advances in Pure Mathematics, Vol. 3 No. 7, 2013, pp. 639-642. doi: 10.4236/apm.2013.37084.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] L. A. Zadeh, “Fuzzy Sets,” Information and Control, Vol. 8, No. 3, 1965, pp. 338-353.
http://dx.doi.org/10.1016/S0019-9958(65)90241-X
[2] C. L. Chang, “Fuzzy Topological Spaces,” Journal of Mathematical Analysis and Applications, Vol. 24, No. 1, 1968, pp. 265-270.
http://dx.doi.org/10.1016/0022-247X(68)90057-7
[3] R. Lowen, “Fuzzy Topological Spaces and Fuzzy Compactness,” Journal of Mathematical Analysis and Applications, Vol. 56, No. 3, 1976, pp. 621-633.
http://dx.doi.org/10.1016/0022-247X(76)90029-9
[4] T. E. Gantner, R. C. Steinlage and H. R. Warren, “Compactness in Fuzzy Topological Spaces,” Journal of Mathematical Analysis and Applications, Vol. 62, No. 3, 1978, pp. 547-562.
http://dx.doi.org/10.1016/0022-247X(78)90148-8
[5] A. S. Mashhour andM. H. Ghanim, “Fuzzy Closure Spaces,” Journal of Mathematical Analysis and Applications, Vol. 106, No. 3, 1985, pp. 154-170.
http://dx.doi.org/10.1016/0022-247X(85)90138-6
[6] W. J. Thron, “What Results Are Valid on Cech-Closure Spaces,” Topology Proceedings, Vol. 6, 1981, pp. 135-158.

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.