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Let A is the rectangular hyperbola xy=1 and B is the union of axes xy=0.find d(A,B).

Now if A and B be two non-empty subset of a metric space X then d(A,B)=inf{d(a,b): a $\in$ A and b $\in$ B}. Honestly I didn't understand this question and have no idea how to proceed.

Sinchan Bhattacharjee
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1 Answers1

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For $x>0$, $(x,\frac{1}{x})$ is in $A$. It is at distance $\frac{1}{x}$ of $B$. So, what is the infimum of such distances ?

Didier
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