Definition:Disconnected Space/Definition 2
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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
- 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