Let M be a smooth manifold. Let's call M quasi-seperated if M has the following property: If B,CsubseteqM are open balls, then BcapCsubseteqM is a finite(!) union of open balls. By an open ball I mean an open submanifold, which is diffeomorphic to some Dn.
Is every manifold quasi-separated? If not, are open balls quasi-separated? Is there a simple characterization of quasi-separated manifolds?
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