Definition:Nowhere Dense

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

Let $H \subseteq S$.

Equivalence of Definitions
These definitions can be seen to be directly equivalent from the definition of interior as the union of all subsets of $H$ open in $T$.

Example

 * Set of Reciprocals of Positive Integers is Nowhere Dense in Reals

Also see

 * Everywhere dense
 * Dense-in-itself