Existence of a surjective map between the two space $X$ and $C([a,b],X)$

Question

Let $X$ a Hilbert space and $C\left(\left[a,b\right],X\right)$ the space of Continuous functions from $\left[a,b\right]$ into $X$. My question is as follows: is there exists any surjectif map from $C\left(\left[a,b\right],X\right)\rightarrow X$. Thank you for your help!

Answer 1

$f \to f(a)$ is such a map. Note that given $x\in X$ the constant map $f(y)=x$ for all $y$ is an element of $C([a,b],X)$