For some reason I am having trouble parsing this bit from Guillemin & Pollack Chapter 2.4:
Let $X, Z$ be transversal closed submanifolds in $Y$ (everything is without boundary). Further, let $X$ be compact. Then, $X \cap Z$ is compact and zero-dimensional. I want to show its finite.
Normally, such proofs should go like if it was infinite then some subsequence satisfying some property would have a limit point, which would be contained in the set and would violate something or the other.
Thanks for the help.