Theorem
1
[2FW]Let \(φ: [0,1] → ℝ^ 2\) be simple closed curve in the plane and \(C=φ([0,1])\) be its trace. (See [1PB] for the definition). The complement \(ℝ^ 2 ⧵ C\) consists of exactly two connected components, that are open. One of these components is bounded (and is called “the interior of the curve”, or, “the region bounded by the curve”) and the other is unbounded (the exterior). The curve \(C\) is the boundary of each component.