Let A and B be two non-empty disjoint subsets of R and let d(A,B)=infa-b:ain A,bin B. Then d(A,B)0 if:

(C) A is closed and B is compact

Q15Section II (Mathematics)15 of 190

Compactness, not mere closedness, guarantees positive distance to a disjoint closed set

Let A and B be two non-empty disjoint subsets of $\mathbb{R}$ and let $d(A,B)=\inf\{|a-b|:a\in A,b\in B\}$ . Then $d(A,B)>0$ if:

Pick an option to check your answer.

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