Definition:Connected (Topology)/Topological Space/Definition 3

Definition

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

$T$ is connected if and only if its only subsets whose boundary is empty are $S$ and $\O$.

Also see

• Equivalence of Definitions of Connected Topological Space

• Results about connected spaces can be found here.

Sources

• 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): Exercise $6.6.2$