For a continuous map 
, the nonwandering set 
is the subset of 
consisting of all nonwandering
points. Equivalently, 
if every open neighborhood 
of 
satisfies
 |
for some positive integer 
.
The nonwandering set is closed and forward invariant under 
.
If 
is a homeomorphism, then 
. Every periodic
point is nonwandering, so the closure
of the set of periodic points is contained in 
, although equality need not hold.
