  We extend the notion of a dyadic grid of cubes in Euclidean space to include
infinite dyadic cubes. These `tops' of a dyadic grid form a tiling of Euclidean
space which is subject to the constraints similar to those arising in tiling
Euclidean space by (finite) unit cubes. These tops arise in the theory of two
weight norm inequalities through weighted Haar and Alpert wavelets.
