Wild arc

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The Fox-Artin wild arc lying in R3 Note that each "tail" of the arc is converging to a point.

In geometric topology, a wild arc is an embedding of the unit interval into 3-dimensional space not equivalent to the usual one in the sense that there does not exist an ambient isotopy taking the arc to a straight line segment. Antoine (1920) found the first example of a wild arc, and Fox & Artin (1948) found another example called the Fox–Artin arc whose complement is not simply connected.

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