# Definition
A [[Topological Space|topological space]] is **connected** if it is not a union of two non-empty [[Open Sets|open sets]].

i.e. if you draw the two non-empty [[Open Sets|open sets]] on the graph, if you have to lift your pen, it will not be connected.

# Examples
Not connected:
$$\langle 0, 1 ]  \cup [ 2, 5 \rangle$$
Connected:
$$\langle 0, 1 ] \cup [ 0.5, 5 \rangle = \langle 0, 5 \rangle$$