Double Topologists's Sin Curve

The Double Topologists's Sin Curve is defined by the union

$$\{(x,y) \in R^2 : 0 < \vert x\vert \le 1 , y=\sin(1/x)\} \cup \{(0,y) \in R^2 : -1 \le y \le 1 \} \quad .$$

It has just three path components.

Double Topologists's Sin Curve- fig. a


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