What is an open surface bounded by a closed contour

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Can someone tell me what an open surface bounded by a closed contour is please? I have difficulties to imagine something.

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How bout $D^o = \{x \in \mathbb{R}^2 : \|x\| < 1\}$? This is an open set, and the closed contour bounding it is precisely $S^1 = \{x \in \mathbb{R}^2 : \|x\| = 1\}$.