Tops of dyadic grids

Abstract: 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.