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Olympiad Combinatorics

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Problems 2

Can you cover the real plane, R2\mathbb{R}^2R2, using a disjoint set of topological T's? \\ [Source: Communicated by Mark Sellke, and separately by David (Ting-Chun) Lin, who he…
Can you cover the real plane, R2\mathbb{R}^2R2, using a disjoint set of topological O's? \\ [Source: Classical?]