Knots are typically seen as embeddings (non self-intersecting image) of S^n, a closed orientable surface. For example, S^1 (the circle) in R^3 (3-dimensional space) is what we usually think of as a knot. The simplest knot, trefoil knot, is just a circle embedded into the ambient space in a way that cannot but &quot;untangled&quot; without self-intersection.<p>The Klein bottle, being non-orientable, is not usually considered a knot.<p>But the important thing is that a knot is all about the ambient space. If you are allowed 4-dimensional motions, then you can always untangle any embedding of S^1.