Let \( X \) be a topological space . A subset \( U \subset X \) is called a component of \( X \) if it is connected and maximal, i.e., there is no connected subset in \( X \) which properly contains \( U \).
Remarks
Let \( X \) be a topological space . A subset \( U \subset X \) is called a component of \( X \) if it is connected and maximal, i.e., there is no connected subset in \( X \) which properly contains \( U \).