Definition:Topologist's Sine Curve

Definition
Let $G = \left\{{\left({x, \sin \dfrac 1 x}\right)} \, \middle | \, {0 < x \le 1}\right\}$, 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.

Also see

 * Definition:Closed Topologist's Sine Curve