Let T be a finite complement topology on . We know that is not closed in (2 is not finite in ).

Let r be a function such that r(2i-1)=r(2i)=2i for each . r is well-defined. For any closed subset A of , is closed in . Thus r is continuous. We also have r(2i)=2i for each i in .

Thus, 2 is a retract of , which is not closed in .