The third symmetric potency (alias: the third finite subset space) of the circle

Bott showed that the space of nonempty subsets of the circle of cardinality at most 3 is homeomorphic to the three sphere and Shchepin showed that the inclusion of the space of one-element subsets is a trefoil knot. We gave an elementary cut-and-paste proof of these results.

Click Here to see a javascript animation.

A paper model

Print this pdf onto a sheet of A4 transparency film and follow this instruction.