A continuous non-intersecting curve in the plane whose origin and terminus coincide?
A Jordan curve is a continuous none-self-intersecting curve whose origin and terminus coincide.
The Jordan curve theorem asserts that every Jordan curve divides the plane into an "interior" region bounded by the curve and an "exterior" region containing all of the nearby and far away exterior points, so that every continuous path connecting a point of one region to a point of the other intersects with that loop somewhere.