Is given metric space $(M, d)$. Let $A\cap B = \emptyset; \,\,\text{dist}(A,B):=\inf\{d(x,y):x\in A, y\in B\}$. $A, B$ are both closed sets. Is it possible that $\text{dist}(A,B)=0$?
The first thought comes into mind is that obviously $\text{dist}(A,B)>0$, but possibly there are some tricky $d$ and $A, B$ so that it's untrue.
Thanks in advance!