Definition:Connected (Topology)/Topological Space/Definition 5

Definition

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

$T$ is connected if and only if there are no two non-empty separated sets whose union is $S$.

Also see

• Equivalence of Definitions of Connected Topological Space

• Results about connected spaces can be found here.

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $4$: Connectedness