TITLE: Cantor space: example of an open set that's not closed?
QUESTION [6 upvotes]: Very basic question: I can't get my head around the Cantor space. It has a basis of clopen sets. Finite unions of closed sets are closed, and unions of open sets are open, so a finite union of basis elements of a Cantor space is clopen. The only open sets in a Cantor space that are not closed, if there are any, are infinite unions of basis elements. An example of an open set that's not closed is ... what? 
Not a homework question; I managed to stump myself. Thanks for your help.

REPLY [2 votes]: Just make a sort of fishbone, and remove the spine: $$\bigcup_{i=1}^{\infty} [10^i].$$