A curve is simple if it does not cross itself.
Simple Curve
See also
Closed Curve, Jordan CurveExplore with Wolfram|Alpha
References
Krantz, S. G. "Closed Curves." §2.1.2 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 19-20, 1999.Referenced on Wolfram|Alpha
Simple CurveCite this as:
Weisstein, Eric W. "Simple Curve." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SimpleCurve.html