please answer #4, reference is down below

4. a. Determine whether the function f; R R" defined by f(t) = (t, }t, It, It, It,...) = (2 "t)po is continuous when R" is equipped with either the product or the box topology. b. Consider the sequence (a,) , C R" defined by (1, 0, 0, 0, 0, 0, . . . ) 02 = (0, 1 0, 0, 0, 0, ...) if n= k (0, 0, , 0, 0, 0, ... ) 0 else a4 (0, 0, 0, 256 , 0, 0, ) Determine in which of the (i) product, (ii) box, and (iii) uniform topologies the sequence (a, ), converges. Briefly justify your answers. Notation and basic conventions. Throughout let X and Y denote topological spaces, and for a subset A of a topological space denote its closure by A and the set of its limit points by A