Let \((E,d)\) be a metric space and \(K\) a subset of \(E\). Then \(K\) is said to be connected if
and only if every subset of \(K\) are only closed
if and only if \(K\) is not the only nonempty set that is open and closed
—>> if and only if it is connected as a subspace
\(K\) is only open
