Tiling Theorem

Due to Lebesgue and Brouwer. If an n-dimensional figure is covered in any way by sufficiently small subregions, then there will exist points which belong to at least n+1 of these subareas. Moreover, it is always possible to find a covering by arbitrarily small regions for which no point will belong to more than n+1 regions.

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Cite this as:

Weisstein, Eric W. "Tiling Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TilingTheorem.html

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