An example of a subspace of the Euclidean plane that is connected but not pathwise-connected with respect to the relative topology. It is formed by the ray , and the graph of the function for . This set contains no path connecting the origin with any point on the graph.

# Topologist's Sine Curve

## See also

Sine
*This entry contributed by Margherita
Barile*

## Explore with Wolfram|Alpha

## References

Joshi, K. D.*Introduction to General Topology.*New Delhi, India: Wiley, pp. 151-153, 1983.Willard, S.

*General Topology.*Reading, MA: Addison-Wesley, p. 198, 1970.

## Referenced on Wolfram|Alpha

Topologist's Sine Curve## Cite this as:

Barile, Margherita. "Topologist's Sine Curve." From *MathWorld*--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/TopologistsSineCurve.html