Definition:Disconnected Set/Definition 3
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Definition
Let $T = \struct {S, \tau}$ be a topological space.
Let $H \subseteq S$ be a non-empty subset of $S$.
$H$ is a disconnected set of $T$ if and only if there exist non-empty subsets $U$ and $V$ of $H$ such that all of the following hold:
- $H = U \cup V$
- no limit point of $U$ is an element of $V$
- no limit point of $V$ is an element of $U$.
Also see
- Results about disconnected sets can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): disconnected set
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): disconnected set