Let X = {0}⋃{1/n|n>0}.
X is a subset of the reals and its <a href=http://en.wikipedia.org/wiki/Subspace_topology>relative topology</a> T is:
x∈T if either<ul>
<li>x is an arbitrary subset of {1/n|n>0}, or
<li>x = {0}⋃v where v is a subset of {1/n|n>0} and ∃n(n>0 &amp; ∀m(m>n → {1/m}∈x)).</ul>
m and n range over integers.