You're contradicting yourself here: "[0,1] is open" needs additional context, but saying that A* (or [A] in your notation) can be written as a rational of a power series (1/(1-A)).
Why? Well, the expression makes sense in a ring, where + has the inverse -. It's an annoying abuse of notation in a semiring, such as the semiring of lists (aka the free monoid over A) because you don't have a -. Your case is even more annoying because you're not distinguishing between list concatenation (associative) and product type (not associative).
In that respect, many mathematicians and physicians write as if PL/I were their language of choice: free type conversion, for everyone, when you least expect it.