Is there a higher dimensional analogue of the Lakes of Wada in $3$, $4$, or more dimensions? For those who don't know, the Lakes of Wada are three disjoint connected open sets in the real plane with the property that all three share the same boundary.
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I believe one of the comments on https://math.stackexchange.com/questions/723666/in-mathbbrn-how-many-disjoint-open-sets-can-share-a-boundary?rq=1 answer this. – Henrik supports the community Oct 04 '23 at 14:31
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1Just take the product of the 2d example with $R^{n-2}$ and get an example in $ R^n$. – Moishe Kohan Oct 04 '23 at 14:39