Write $C[a,b]$ for the real vector space of all continuous functions $[a,b]\to \mathbb{R}.$
I need to show that the infinite-dimensional vector spaces $C[0,1]$ and $C[1,2]$ are isomorphic.
My idea is to define a map $\theta:C[0,1]\to C[1,2]$ like this:
For any $f \in C[0,1],$ we define $\theta(f)$ to be the continuous map $t\mapsto f(t-1)$ on the inverval $[1,2].$
I think this map $\theta$ is an isomorphism of real vector spaces - am I right?