Topologist's Sine Curve
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 w...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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.
