# Connectedness in fuzzy closure space

## DOI:

https://doi.org/10.14419/ijamr.v3i4.3394## Published:

2014-09-26## Abstract

A fuzzy ?ech closure space (X, k) is a fuzzy set X with fuzzy ?ech closure operator k: I^{X} ? I^{X } where I^{X } 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} I^{X } . 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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