Clouds in Higher Dimensions

Samuel Desrochers

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arXiv · 1910.06406

Clouds in Higher Dimensions

Samuel Desrochers

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Abstract

Following some work done by Komjath and Schmerl, we extend the definition of a cloud to $\mathbb{R}^N$ for $N \geq 2$ and show that $k$ clouds cover $\mathbb{R}^2$ if and only if $k$ clouds cover $\mathbb{R}^N$. We also show that countably many clouds cover $\mathbb{R}^N$.

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BibTeX RIS

Samuel Desrochers. 2019-10-14. Clouds in Higher Dimensions. https://arxiv.org/abs/1910.06406

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