math.AT — Algebraic Topology
Singularity Projection in Three-Dimensional Space and the Discretization of a Continuous Interval
We study the projection geometry induced by a singular point on the boundary of a three-dimensional fan-shaped cylinder. The cylinder is defined in the first quadrant of the real coordinate plane, with x and y both between zero and one, and a singular point located at x=1 on the boundary. Through an iterative projection process involving the angle bisector of the quadrant, we prove that the continuous interval [0,1] is precisely discretized to an infinite set of boundary points.
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