In mathematics, a Cantor cube is a topological group of the form {0, 1}A for some index set A.
Cantor cubes are special among compact groups because every compact group is a continuous image of one, although usually not a homomorphic image.
(The literature can be unclear, so for safety, assume all spaces are Hausdorff.)
In fact, every AE(0) space is the continuous image of a Cantor cube, and with some effort one can prove that every compact group is AE(0).
It follows that every zero-dimensional compact group is homeomorphic to a Cantor cube, and every compact group is a continuous image of a Cantor cube.