Definition:Topologist's Sine Curve

Definition
Let $G = \set {\tuple {x, \sin \dfrac 1 x} : 0 < x \le 1}$, considered as a subset of the real number plane with the usual (Euclidean) topology $\struct {\R^2, \tau_d}$.

Then the set $G \cup \set {\tuple {0, 0} }$ is called the Topologist's Sine Curve.

Also see

 * Definition:Closed Topologist's Sine Curve