 to represent an intrinsic property of C. The second difficulty is that closed curves do not correspond uniquely to regions of space: e.g., circling the region in which there is a magnetic field twice on the same circle will produce a different curve from circling it once. But this does not prevent one from taking \(S(C)\) at some time to represent an intrinsic property of a loop—the oriented region of space traced out by a closed curve C that intersects itself only at its end-point.