Trefoil Knot is Homeomorphic to Circle

Theorem

The trefoil knot is homeomorphic to the circle.

Proof

Despite the fact that you cannot actually rearrange a trefoil knot actually into a circle in the usual $\R^3$ space, you can set up a mappping from one to the other.

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Sources

• 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $3$: Continuity generalized: topological spaces: $3.6$: Homeomorphisms: Examples $3.6.2 \ \text{(f)}$