EDIT: of course the replies are correct. i suppose it was unclear what the parent meant by "anonymous functions". if he meant lambdas, then they are indeed closures but without the same capabilities as normal python functions. their capabilities are unrelated to the fact that they're anonymous or closures.
Technically Python has what I like to call "Java closures" (although I admit that is not really fair). In Python the body of an anonymous function (lambda) can only be an expression and the bindings closed over by a named inner function are immutable. You can get around the second limitation with a single element list and this is the same way you get around Java's limitation that a local variable referenced by an anonymous inner class be final.
Python 3 has full featured closures. In Python 2 it is not possible to alter what a variable references. It's still possible to alter the contents of the object being referenced leading to the "put the value in a list" type of hackery to simulate full featured closures.