Prove whether the following is true or false. If it is false give a counter example.
If M is a connected point set, the cl(M) is connected.
There is a basic lemma that says: If the sets C and D form a separation of X, and if Y is a connected subset of X, then Y lies entirely within either C or D. Call this "Lemma A".
Suppose cl(M) is not connected. Then cl(M) = C U D ...
This is a proof regarding connected point sets.