Let S and T be subsets of R. find a counterexample for each of the following:
a) If p is the set of all isolated points of S, then p is a closed set.
d) bd(cl S) = bd S
See what you can do with these.
$\displaystyle \begin{gathered}
a)\quad S = \left\{ {\frac{1}
{n}:n \in \mathbb{Z}^ + } \right\} \hfill \\
d)\quad T = (0,1) \cup (1,2) \hfill \\
\end{gathered} $