Definition:Dense-in-itself

Definition

Let $T = \left({S, \tau}\right)$ be a topological space.

Let $H \subseteq S$.

Then $H$ is dense-in-itself iff it contains no isolated points of $H$.

Also see

• Everywhere dense
• Nowhere dense

• Results about topological denseness can be found here.

Sources

• Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (1970)... (previous)... (next): $\text{I}: \ \S 1$: Limit Points