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On smooth fuzzy subspaces

We introduce a new concept of smooth topological subspaces, which 
coincides with the usual definition in the case where μ = χ Y , Y ⊂ X . Also, we introduce some concepts such 
as q -nbd systems, continuity, separation 
axioms, compactness, and connectedness in this sense. Also, 
various characterization for some fuzzy topological concepts in 
this sense are given.