A fundamental domain of a group 
in a topological G-set 
is a closed subset 
of 
such that 
is the union of conjugates of 
, i.e.,
 |
and the intersection of any two conjugates has no interior. The 
-action on 
therefore covers 
by the conjugates of 
while permitting them to overlap only on sets with empty interior.
For example, a fundamental domain of the group of rotations by multiples of 
in 
is the upper half-plane 
and a fundamental domain
of rotations by multiples of 
is the first quadrant 
.
The concept of a fundamental domain is a generalization of a minimal group block, since while the intersection of fundamental domains has empty interior, the intersection of minimal blocks is the empty set.
