(Solved): (3) (0.5 pt) Let X be endowed with metric dx and Y be endowed with metric dy. Write down the defin ...

(3) (0.5 pt) Let X be endowed with metric dx and Y be endowed with metric dy. Write down the definition of f: X? Y being continuous, in terms of -d language. (4*) (1.5 pts) Under the setting of (3), show that f is continuous if and only if f-¹(U) is open for any open U CY.