Let MM be a smooth manifold. Let's call MM quasi-seperated if MM has the following property: If B,CsubseteqMB,CsubseteqM are open balls, then BcapCsubseteqMBcapCsubseteqM is a finite(!) union of open balls. By an open ball I mean an open submanifold, which is diffeomorphic to some DnDn.
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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