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

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.): Part $\text {II}$: Counterexamples: $116$. Topologist's Sine Curve