# Definition A [[Topological Space]] $(X, \mathcal{T})$ is connected if it cannot be written as $X = X_1 \cup X_2$, where $X_1$ and $X_2$ are both [[open set|open]] and $X_1 \cap X_2 = \emptyset$. Otherwise, $X$ is called disconnected. Below is an example from Wikipedia. A, B, C and D are connected, while $E = \bigcap_{i=1}^4 E_i$ is disconnected. ![[Simply_connected,_connected,_and_non-connected_spaces.svg|400]] Note that $S^n$, the $n-sphere$, is connected.