I've been trying really hard to solve this problem:
Let $C^1(\mathbb{R})$ be the space of continuous functions with continuous derivatives. Show that $C^1(\mathbb{R})$ is normal.
Def: A topological space X is called normal if it is Hausdorff and any two closed disjoint subsets can be seperated topologically.
Def: A topological space (X,T) is Hausdorff if for any x,y in X, there are neighbourhood V of x and W of y, such that that V and W don't intersect.
When I start working with neighbourhoods, I'm pretty sure I need to know how the topology T is defined. This topology isn't defined in the question, and I can't think of a way to continue.
So the main question are which topology is used, or if this is irrelevant and if so, why?
I've researched quite a lot, but in vain. I hope someone here can help me!