Is it true that in Python the closure will persist if and only if it is mentioned by lexicaly in the return value

Let's say I have Python2 code

def foo(n):
    bar = n
    def dispatch(exp):
        return eval(exp)
    return dispatch

foo(10)("bar * 2")  # throw NameError

      

        
        
        
      

    

It seems that the closure is bar

not being persisted. I am assuming it is not shown in the return function

On the other hand, if I mentioned bar

in the return function, although I did nothing, it is saved as a closure

def foo(n):
    bar = n
    def dispatch(exp):
        if bar:
            pass
        return eval(exp)
    return dispatch

foo(10)("bar * 2")  # return 20

      

        
        
        
      

    

Did I understand correctly? This also applies to other languages ​​that support closures, such as JavaScript, Scheme, ...