On the cromatic number of infinitesimal plane layer
2015
We consider natural generalization of plane chromatic number problem. We consider chromatic numbers $\chi$ of spaces $\mathbb{R}^n \times [0,\varepsilon]^k$ for arbitrary small $\varepsilon$.
We prove that $5 \leq\chi(\mathbb{R}^2\times [0,\varepsilon])\leq 7$ and ${6\leq \chi(\mathbb{R}^2\times [0,\varepsilon]^2) \leq 7}$.
Also we consider natural questions, arising from this considerations.
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