Definition:Isolated Point (Topology)/Subset/Definition 2

Definition

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

Let $H \subseteq S$ be a subset of $S$.

$x \in H$ is an isolated point of $H$ if and only if $x$ is not a limit point of $H$.

That is, if and only if $x$ is not in the derived set of $H$.

Also see

• Equivalence of Definitions of Isolated Point

• Results about isolated points can be found here.

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $1$: General Introduction: Limit Points