• Published : 2008.11.30


In this paper, we introduce the relatively new notion of fuzzy ${\omega}^O$-open set. We prove that the collection of all fuzzy ${\omega}^O$-open subsets of a fuzzy topological space forms a fuzzy topology that is finer than the original one. Several characterizations and properties of this class are also given as well as connections to other well-known "fuzzy generalized open" subsets.


  1. M. K. Chakrabarty and T. M. G. Ahsanullah, Fuzzy topology on fuzzy sets and tolerance topology, Fuzzy Sets and Systems 45 (1992), no. 1, 103-108
  2. C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl. 24 (1968), 182-190
  3. A. K. Chaudhuri and P. Das, Some results on fuzzy topology on fuzzy sets, Fuzzy Sets and Systems 56 (1993), no. 3, 331-336
  4. A. H. E¸s, Almost compactness and near compactness in fuzzy topological spaces, Fuzzy Sets and Systems 22 (1987), no. 3, 289-295
  5. T. E. Gantner and R. C. Steinlange, Compactness in fuzzy topological spaces, J. Math. Anal. Appl. 62 (1978), no. 3, 547-562
  6. F. S. Mahmoud, M. A. Fath Alla, and S. M. Abd Ellah, Fuzzy topology on fuzzy sets: fuzzy semicontinuity and fuzzy semiseparation axioms, Appl. Math. Comput. 153 (2004), no. 1, 127-140
  7. C. K. Wong, Covering properties of fuzzy topological spaces, J. Math. Anal. Appl. 43 (1973), 697-704
  8. C. K. Wong, Fuzzy points and local properties of fuzzy topology, J. Math. Anal. Appl. 46 (1974), 316-328

Cited by

  1. Fuzzy W-closed sets vol.4, pp.1, 2017,