Connectedness in fuzzy closure space - Tapi, U. D.; Deole, Bhagyashri (International Journal of Applied Mathematical Research, 2014)
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.