Definition:Everywhere Dense

Let $$T$$ be a topological space.

Let $$H \subseteq T$$.

Then $$H$$ is (everywhere) dense in $$T$$ if:
 * $$\operatorname{cl}\left({H}\right) = T$$.

where $$\operatorname{cl}\left({H}\right)$$ is the closure of $$H$$.

Also see

 * Compare nowhere dense.