Let $(E,d)$ be a metric space, $A,B\subseteq E$ and $a\in A$. If $A$ is compact and $B$ closed and I find a sequence $b_n$ in $B$ so that $d(a,b_n)\rightarrow 0 $, is there any way to conclude that $a \in B$?
2026-03-29 03:21:45.1774754505
A problem in a metric space involving limits
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$d(a,b_n) \to 0$ means $b_n \to a$. Since $B$ is closed $a \in B$.