Abstract
In this paper the structure of fuzzy Banach manifolds has been enriched by inducing three different equivalence relations on fuzzy Banach atlases. Also a Network fuzzy Banach manifold has been defined admitting two equivalence relation and two group structures. Further we define fuzzy smooth homotopy on fuzzy Banach manifold and the study has been extended for three different fuzzy path connectedness inducing equivalence relations and fundamental group structure which is invariant under fuzzy homeomorphism.
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