A topological space is said to be connected if there is no pair of nonempty subsets such that both and are open in , and . If is not connected, i.e. if there are sets and with the above properties, then we say that is disconnected.
Every topological space can be viewed as a collection of subspaces each of which are connected. These subspaces are called the connected components of . Slightly more rigorously, we define an equivalence relation on points in by declaring that if there is a connected subset of such that and both lie in . Then a connected component of is defined to be an equivalence class under this relation.
|Date of creation||2013-03-22 12:00:11|
|Last modified on||2013-03-22 12:00:11|
|Last modified by||mathcam (2727)|