Let $X$ be a topological space and $E_n(X)$ the space of finite sets of cardinality $\leq n$. It is a theorem of Bott that $E_3(S^1)=S^3$. What is the idea to show that the embedding $S^1\hookrightarrow E_3(S^1)$ sending $x$ to the set $\{ x\}$ is the trefoil knot?
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