Connected

Definition

A topological space is connected if it is not a union of two non-empty open sets.

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

Examples

Not connected: $⟨0,1]\cup [2,5⟩$ Connected: $⟨0,1]\cup [0.5,5⟩=⟨0,5⟩$