I want to show that if $w$ is a $p$-form such that its induced cochain on $p$-chains:

$w(\gamma)= \int_{\gamma} w \in S$

takes values in a discrete set $S \subset \mathbb{R}$ then $w$ must be zero.

- My idea is to say that we know some chains (i.e. the zero chain) will integrate to zero and that there is a way to continuously vary the chain so that the value $w(\gamma)$ should vary continuously as well; hitting values outside of $S$.

Any suggestions or ideas are greatly appreciated!

Thanks, CM