Definition:Disconnected Space/Definition 2

Definition

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

$T$ is disconnected if and only if there exist non-empty open sets $U, V \in \tau$ such that:

$S = U \cup V$

$U \cap V = \O$

That is, if there exists a partition of $S$ into open sets of $T$.

Also see

• Equivalence of Definitions of Disconnected Space

• Results about disconnected spaces can be found here.

Sources

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