What are some closed, disjoint subsets $A, B$ in $R^2$ where $inf\{d(A, B) = 0 \forall a \in A \forall b \in B\}$?
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5How about the graph of the equation $xy=1$ and the x-axis? – Old John Oct 25 '13 at 20:35
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1Did you try and search the site before posting the question? – Asaf Karagila Oct 25 '13 at 20:36
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@OldJohn is it closed by ($0, \infty$)? That's open. Please clarify why that works. – Don Larynx Oct 25 '13 at 20:52
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@DonLarynx The x-axis is the set $(-\infty, \infty)$ in $\mathbb{R}^2$, and this is clearly closed. – Old John Oct 25 '13 at 20:55
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@OldJohn if it was closed why isn't it denoted by $[\infty, \infty]$? – Don Larynx Oct 26 '13 at 14:25
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@DonLarynx because $\infty$ does not belong to $\mathbb{R}$. It only belongs to the set of extended real numbers. – Old John Oct 26 '13 at 14:30
