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 if and only if it contains no isolated points.

Also see

• Definition:Everywhere Dense
• Definition:Nowhere Dense

• Results about topological denseness can be found here.

Sources

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