Let X = {0}⋃{1/n|n>0}. X is a subset of the reals and its
relative topology
T is: x∈T if either
x is an arbitrary subset of {1/n|n>0}, or
x = {0}⋃v where v is a subset of {1/n|n>0} and ∃n(n>0 & ∀m(m>n → {1/m}∈x)).
m and n range over integers.