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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

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up vote 0 down vote accepted

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

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