Solution
= Solution
If $x\ne b$, then $d_a(b,x)=d(b,a)+d(a,x)\geq d(b,a)$, so no such $x$ lies in the strict <open ball>. Its centre always does. Hence
$$
\boxed{B_{d_a}(b,d(b,a))=\{b\}}.
$$
Thus every point other than $a$ is isolated.
= Solution
If $x\ne b$, then $d_a(b,x)=d(b,a)+d(a,x)\geq d(b,a)$, so no such $x$ lies in the strict <open ball>. Its centre always does. Hence
$$
\boxed{B_{d_a}(b,d(b,a))=\{b\}}.
$$
Thus every point other than $a$ is isolated.