# Let \((E,d)\) be a metric space and \(K\) a subset of \(E\). Then \(K\) is said to be connected if

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