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Possible Duplicate:
Example to show the distance between two closed sets can be 0 even if the two sets are disjoint

Let $(X,d)$ be a metric space and $A,B$ be two distinct closed set in $X$ such that $dist(A,B)=0$. Does it imply $A\cap B=\emptyset$ ?

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    By choosing $A=B$ we see that it does not imply. Did you mean instead that does it imply $A\cap B\neq \emptyset$?2012-05-16
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    @GEdgar: At present, no, it's just a triviality.2012-05-16

2 Answers 2