Viewing topic: Dunce Cap

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Dunce Cap

  • Definition: Let n be a positive integer with n > 1. Let f: S^1 -> S^1 be rotation through the angle 2pi/n, mapping the point (cos x, sin x) to the point (cos(x + 2pi/n), sin(x + 2pi/n))> Form a quotient space X from the unit ball B^2 by identifying each point of x of S^1 with the points r(x), r^2(x), ... , r^(n-1)(x). Then X is a compact Hausdorff space called the n-fold dunce cap.

    Source: Topology (second edition) by James R. Munkres

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