Definition:Nowhere Dense

Definition
Let $$T$$ be a topological space.

Let $$H \subseteq T$$.

Then $$H$$ is nowhere dense in $$T$$ iff $$\operatorname{Int} \left({\operatorname{cl} \left({H}\right)}\right) = \varnothing$$.

That is, if the interior of its closure is empty, i.e. it is "all boundary".

Example
The set $$\left\{{\frac 1 n: n \in \N}\right\}$$ is nowhere dense in $$\R$$.

Also see

 * Compare dense.