Prove or disprove compactness for a subset of $C([0,1])$ Consider $$A = \{ p : \text{$p$ is a polynomial of degree less than $d$ such that} \max_{x \in [0,1]} |p(x)| \leq 1 \},$$
where $d \in \mathbb{N}.$ I need to prove or disprove compactness of $A$.
I know that $\{ f \in C([0,1]) : \max_{x \in [0,1]} |f(x)| \leq 1 \}$ is not compact. But I'm not sure how restricting to polynomials of degree less than $d$ changes anything.

Hint : set $B = \{ p : \text{$p$ polynomial of degree less than $d$} \}$
then $B$ is a finite dimension subspace of $C[0,1]$ so it is closed.
And hence $A$ is bounded and closed subset of $B.$
And thanks to Heine Borel theorem !  
