Definition:Topologist's Sine Curve

Definition
Let $G = \left\{{ \left({x, \sin \dfrac 1 x}\right) } \mid { 0 < x \le 1 }\right\}$, considered as a subset of the Euclidean space $\R^2$ equipped with the Euclidean topology.

Then the set $G \cup \left\{{ \left({ 0, 0 }\right) }\right\}$ is called the Topologist's Sine Curve.