Pictured at the beginning of every page on this site is the topologist's sine curve, so named because it's a textbook example of why pedestrian's don't bother with such abstract nonsense. It's the graph of the function \(f:(0, 1] \rightarrow \mathbb{R}\) plus the origin \((0, 0)\) defined by \[f(x) = sin(1/x)\]. If we define the following notions:
a set \(X\) of points \(x\) together with a function
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