Suppose \( X \) is a topological space . Each component of \( X \) is closed .
Proof
Let \( B \subset X \) be a component of \( X \). Then
\( B \subset \overline{B} \) is connected according to (0x681ad42b)
.
Since \( B \) is maximal, \( \overline{B} = B \), so \( B \) is closed.