Connected space
![Connected and disconnected subspaces of R²From top to bottom: red space A, pink space B, yellow space C and orange space D are all connected, whereas green space E (made of subsets E1, E2, E3, and E4) is not connected. Furthermore, A and B are also simply connected (genus 0), while C and D are not: C has genus 1 and D has genus 4.](/Images/godic/202502/01/Simply_connected,_connected,_and_non-connected_spaces.svg2142.png")
![This subspace of R² is path-connected, because a path can be drawn between any two points in the space.](/Images/godic/202502/01/Path-connected_space.svg2142.png")
![Examples of unions and intersections of connected sets](/Images/godic/202502/01/Union_et_intersection_d'ensembles.svg2143.png")
![Each ellipse is a connected set, but the union is not connected, since it can be partitioned to two disjoint open sets U and V.](/Images/godic/202502/01/Disconnected-union-of-connected-sets2143.png")
In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint nonempty open subsets. Connectedness is one of the principal topological properties that is used to distinguish topological spaces. A stronger notion is that of a path-connected space, which is a space where any two points can be joined by a path.