On page 6 of the introduction, they state
Indeed consider the de Rham theory of $\mathbb{R}^1$ with compactly supported forms. Clearly the only function with compact support on $\mathbb{R}^1$ is the zero function.
I just started reading about this, so I bet I am missing something. What about bump functions like the ones described here https://en.wikipedia.org/wiki/Bump_function? Don't they contain a compactly supported function defined on the real line?
They mean only function that is locally constant function with compact support is the zero function.