By definition $\operatorname{Spec}k$ is a point for any field $k$. So $\operatorname{Spec}\mathbb{Q}, \operatorname{Spec}\mathbb{R}, \operatorname{Spec}\mathbb{C}$ etc are all the same as topological spaces. But according to the natural inclusion map $$ \mathbb{Q} \rightarrow \mathbb{R} \rightarrow \mathbb{C} $$ there exist natural morphisms $$ \operatorname{Spec}\mathbb{Q} \leftarrow \operatorname{Spec}\mathbb{R} \leftarrow \operatorname{Spec}\mathbb{C}, $$ but not the other direction. So $\{\operatorname{Spec}k\}_k$ must carries more information than merely one point topological space.
I would appreciate it if someone could kindly explain what is going on.