Connectedness in fuzzy closure space


  • U. D. Tapi
  • Bhagyashri Deole Affiliated by D.A.V.V. Indore (M.P.) India





A fuzzy ?ech closure space (X, k) is a fuzzy set X with fuzzy ?ech closure operator k: IX ? IX where IX is a power set of fuzzy subsets of  X, which satisfies k ( ) = , 1 ?2 ? k( 1 )  k( ?2 ), k ( 1 ?2 ) =  k 1) ?k (?2)  for all 1 , ?2 IX . A fuzzy topological space X is said to be fuzzy connected if it has no proper fuzzy clopen set.Many properties which hold in fuzzy topological space hold in fuzzy ?ech closure space as well. A ?ech closure space (X, u) is said to be connected if and only if any continuous map f from X to the discrete space {0, 1} is constant. In this paper we introduce connectedness in fuzzy ?ech closure space.

Keywords: Connectedness in Fuzzy ?ech Closure Space, Connectedness in Fuzzy Topological Space, Fuzzy ?ech Closure Operator, Fuzzy ?ech Closure Space, Fuzzy Topological Space.


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