Q:

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]

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

A:

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

