Solution
= Solution
\b[False.] The subspace
$$
X=\{0\}\cup\{1/n:n\geq1\}\subset\mathbb R
$$
is closed and hence complete, and it is countable; however, $0$ is not isolated.
= Solution
\b[False.] The subspace
$$
X=\{0\}\cup\{1/n:n\geq1\}\subset\mathbb R
$$
is closed and hence complete, and it is countable; however, $0$ is not isolated.