Check if max(L) is closed or not for max(L) : { w| w is in L but no x other than EmptyString, wx is in L }.

Correct if Logic is wrong.,

If wx is not in L ( except x is empty ) i.e. x forces the flow to stop at a non-Final state. So unless x is Empty, constructing a dfa for wx is not possible and by definition if x is Empty wx lands on a final state, so is w alone.

A dfa is possible for all ‘w’ in L => dfa is possible for ‘w’ for max(L) => Closed.