This is a Pure Math question.

(5 marks) Let f = {f1, f2, ..., fN} be an N-map IFS over a subset D E R", i.e., the fk : D - D are contraction maps with contraction factors Ck E [0, 1). From the Theorem given in Lecture 34 of the lecture notes, there exists a unique set A such that f ( A ) = A , (18) where f denotes the "parallel" operator associated with this IFS. Let Xx be a fixed point of IFS map fr for any k E {1, 2, ..., N}. Prove that TK E A. You should state any Theorems from the course (Lecture Notes) that you use in your proof