Editing Nowhere dense set (section)

== Examples ==

* The set <math>S=\{1/n:n=1,2,...\}</math> and its closure <math>S\cup\{0\}</math> are nowhere dense in <math>\R,</math> since the closure has empty interior.
* The [[Cantor set]] is an uncountable nowhere dense set in <math>\R.</math>
* <math>\R</math> viewed as the horizontal axis in the Euclidean plane is nowhere dense in <math>\R^2.</math>
* <math>\Z</math> is nowhere dense in <math>\R</math> but the rationals <math>\Q</math> are not (they are dense everywhere).
* <math>\Z \cup [(a, b) \cap \Q]</math> is '''{{em|not}}''' nowhere dense in <math>\R</math>: it is dense in the open interval <math>(a,b),</math> and in particular the interior of its closure is <math>(a,b).</math>
* The empty set is nowhere dense.  In a [[discrete space]], the empty set is the {{em|only}} nowhere dense set.{{sfn|Narici|Beckenstein|2011|loc=Example 11.5.3(a)}}
* In a [[T1 space|T<sub>1</sub> space]], any singleton set that is not an [[isolated point]] is nowhere dense.
* A [[vector subspace]] of a [[topological vector space]] is either dense or nowhere dense.{{sfn|Narici|Beckenstein|2011|loc=Example 11.5.3(f)}}