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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?

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  • $\begingroup$ Can you take a photo of that Page and post here $\endgroup$ – Praphulla Koushik Nov 2 at 16:27
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enter image description here

They mean only function that is locally constant function with compact support is the zero function.

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