High Quality Content by WIKIPEDIA articles! In the branch of mathematics known as topology, the topologist's sine curve is a topological space with several interesting properties that make it an important textbook example. The topologist's sine curve can be defined as the graph of the function sin(1/x) over the interval (0, 1] extended by the origin, under the topology induced from the Euclidean plane. As x approaches zero, 1/x approaches infinity at an increasing rate. This is why the frequency of the sine wave increases on the left side of the graph.

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