Definition:Disconnected Set/Definition 2

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 open sets $U$ and $V$ of $T$ such that all of the following hold:

$H \subseteq U \cup V$

$H \cap U \cap V = \O$

$U \cap H \ne \O$

$V \cap H \ne \O$

Also see

• Equivalence of Definitions of Disconnected Set

• Results about disconnected sets can be found here.

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