Let \(X\) be a topological space. A set \(A\subseteq X\) is nowhere dense in \(X\) if its closure has empty interior: \(\qty{\overline{A}}^\circ=\emptyset\).
Equivalently, \(A\) is not dense in any nonempty open subset of \(X\). For \(X=\RR\), a set \(A\) is nowhere dense if and only if every open interval \(I\) contains an open subinterval \(S\subseteq I\) with \(S\cap A = \emptyset\), that is, \(\overline{A}\) contains no open interval.
In \(\RR\), the sets \(\theset{1/n \suchthat n\geq 1}\) and \(\ZZ\) are nowhere dense: their closures \(\theset{0}\cup\theset{1/n\suchthat n\geq 1}\) and \(\ZZ\) contain no open interval. The sets \(\QQ\) and \(\ZZ\cup\qty{(a, b)\cap \QQ}\) with \(a<b\) are not nowhere dense: their closures contain \(\RR\) and \([a,b]\) respectively.