# Closed sets in Cantor Space that are not Clopen

1. Aug 5, 2011

### Bacle

Hi,

Is there a characterization of subsets of the Cantor space C that are closed but not open? As a totally-disconnected set/space, C has a basis of clopen sets; but I'm just curious of what the closed non-open sets are.

2. Aug 10, 2011

### Eynstone

I guess the subsets which don't contain a 'part' of C ( i.e. a small copy of C) are among such sets.These include the subsets containing finitely many points; which are closed but not open.