How to find Partition of unity in $\mathbb{S}^n$ with only $2$ functions?
2026-03-26 11:17:29.1774523849
How to find Partition of unity in $ \mathbb{S}^n$ with only $2$ functions
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HINT: Do this on $S^1=\Bbb R\cup\{\infty\}$ first and then modify (replacing $x$ with $\|x\|$) adapt to $S^n$. I assume you know the standard construction of bump functions.