Definition:Connected (Topology)/Topological Space/Definition 1

Definition
Let $T = \struct {S, \tau}$ be a topological space.

$T$ is connected it admits no separation.

That is, $T$ is connected there exist no open sets $A, B \in \tau$ such that $A, B \ne \O$, $A \cup B = S$ and $A \cap B = \O$.

Also see

 * Equivalence of Definitions of Connected Topological Space