Given a closed curve in 2D space that intersects itself (transversally, and there's no point in which three paths or more meet), is it possible to look at it as a Celtic knot so when you follow it, one time you're above the other path in an intersection point, and one time you're under it?
My gut feeling tells me it is possible, but I could not proof it. Any idea?
For example this closed curve has been drawn so the crossings alternate over-under-over-under: