if I have a CW-complex $K$ and a subcomplex $L$, what can I say about an $n$-cell $K_{\sigma}$ if its intersection with $L$ is non-empty and not contained in the $(n-1)$-skeleton $K^{(n-1)}$? Does $K_{\sigma}$ have to be in $L$?
I know that then the intersection of $K_{\sigma}$ with $L$ contains an open subset of $K_{\sigma}$. But I don't know if it tells us anything more.
Thank you!