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Set dense

Source: KöMaL A. 775

April 5, 2021
geometry

Problem Statement

Let HāŠ†R3H\subseteq\mathbb{R}^3 such that if we reflect any point in HH across another point of HH, the resulting point is also in HH. Prove that either HH is dense in R3{R}^3 or one can find equidistant parallel planes which cover HH
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