Definition:Connected (Topology)/Topological Space/Definition 7

Definition

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

$T$ is connected if and only if:

there do not exist disjoint, non-empty open sets $X$ and $Y$ of $T$ such that $X \cup Y = S$.

Also see

• Equivalence of Definitions of Connected Topological Space

• Results about connected spaces can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): connected space
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): connected space