Let P denote the set of all polynomials in the real variable x which varies over the interval [0, 1]. What is the closure of P in C[0, 1]

Question

Let P denote the set of all polynomials in the real variable x which varies over the interval [0, 1]. What is the closure of P in C[0, 1] (with its usual supnorm topology)

please help. no idea how to solve this

Answer 1

Hint: Look up the Stone-Weierstrass Theorem. (For your problem, the Weierstrass Approximation Theorem suffices.)