A topological space X is said to be disconnected space if X can be separated as the union of two non-empty disjoint open sets.
            In other words, a topological space X is said to be a disconnected space if there exist non-empty open sets A and B such that  and . The pair  is called the disconnection of X.

Example:
            Show that two point discrete spaces is disconnected.
            Let X be a two point discrete space, If A is any proper subset of X, then both  and  are non-empty open subsets of X such that  and . This shows that  is a disconnection of X, so X is a disconnected space.

Examples:

•  is a disconnected.
•  with upper limit topology is disconnected, since  and  are both open sets which form a disconnection of .
• Let  be a non-empty set, with topology  defined on X. Then  is a disconnected space.
• Every discrete space with more than one point is disconnected.