Definition: A component of a topological space X is a connected subset C of X which is not a proper subset of any connected subset of X. The following properties of the components of a space X should be noted: (1) Each point a eX belongs to exactly one component. The component Ca containing a is the union of all the connected subsets of X which contain a and thus may be thought of as the largest connected subset of X which contains a. (2)For points a, b in X, the components Ca and Cb are either identical or disjoint. (3)Every connected subset of X is contained in a component. (4)Each component of X is a closed set. (5)X is connected if and only if it has only one component. (6)lf C is a component of X and A, B form a separation of X, then C is a subset of A or a subset of B.