Observe that both 
and 
are open and closed in , i.e., clopen.
Proof. Pastime.
Remark. (
‘s in several symbols )
is a set of points.
, the interior of set , contains all interior points.
, the derived set of set , contains all accumulation/cluster/limit points.
, the closure of set , contains all adherent points.
(also denoted by 
or 
), the boundary of set , contains all boundary points.