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typologists
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In the branch of mathematics known as topology, the topologist's sine curve or Warsaw sine curve is a topological space with several interesting properties that make it an important textbook example. * It can be defined as the graph of the function sin(1/x) on the half-open interval (0, 1], together with the origin, under the topology induced from the Euclidean plane: * * * * T * = * * { * * * ( * * x * , * sin * * * * * 1 * x * * * * * ) * * : * x * ∈ * ( * 0 * , * 1 * ] * * } * * ∪ * { * ( * 0 * , * 0 * ) * } * . * * * {\displaystyle T=\left\{\left(x,\sin {\tfrac {1}{x}}\right):x\in (0,1]\right\}\cup \{(0,0)\}.} |