A smooth map whose image has singularities. In particular, in the theory of Vassiliev's knot invariants, singular knots with a finite number of ordinary double points play an important role.
Singular Knot
See also
Ordinary Double Point, Vassiliev InvariantThis entry contributed by Sergei Duzhin
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Duzhin, Sergei. "Singular Knot." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/SingularKnot.html