Notation Question Regarding Function Mapping

Question

When one writes $C([0,1]; \mathbb{R}^d)$, they mean the following, right?

$C([0,1]; \mathbb{R}^d) \equiv \{f: [0,1] \rightarrow \mathbb{R}^d : f \text{ is continuous}\}$

I apologize for the stupidity of this question.

Answer 1

Yes. But while I'm here I'll add that people usually are referring to the set as well as the supremum-norm when they use this notation.