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
This entry contributed by Margherita Barile
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ReferencesJoshi, 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|AlphaTopologist'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