Definition:Connected (Topology)/Topological Space/Definition 2

Definition

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

$T$ is connected if and only if it has no two disjoint nonempty closed sets whose union is $S$.

Also see

• Equivalence of Definitions of Connected Topological Space

• Results about connected spaces can be found here.

Sources

• 2000: John M. Lee: Introduction to Topological Manifolds: $\S 4$ Connectedness and Compactness
• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $4$: Connectedness