> you can put a cd shaped object on
You're thinking of open sets.
In particular, consider two intersecting planes. You can put all the discs you like on that surface, but it's not a manifold because on the line of intersection it's not locally R2.
alt Hacker News
In particular, consider two intersecting planes. You can put all the discs you like on that surface, but it's not a manifold because on the line of intersection it's not locally R2.