Editing Connected space (section)

== Stronger forms of connectedness ==
There are stronger forms of connectedness for [[topological space]]s, for instance: 
* If there exist no two disjoint non-empty open sets in a topological space <math>X</math>, <math>X</math> must be connected, and thus [[hyperconnected space]]s are also connected.
* Since a [[simply connected space]] is, by definition, also required to be path connected, any simply connected space is also connected. If the "path connectedness" requirement is dropped from the definition of simple connectivity, a simply connected space does not need to be connected.
*Yet stronger versions of connectivity include the notion of a [[contractible space]]. Every contractible space is path connected and thus also connected.

In general, any path connected space must be connected but there exist connected spaces that are not path connected. The [[Comb space|deleted comb space]] furnishes such an example, as does the above-mentioned topologist's sine curve.