The theory of digital topology is used in many different image processing and computer graphics algorithms. Most of the existing theories apply to uniform cartesian grids, and they are not readily extensible to new algorithms targeting at adaptive cartesian grids. This article provides a rigorous extension of the classical digital topology framework for adaptive octree grids, including the characterization of adjacency, connected components, and simple points. Motivating examples, proofs of the major propositions, and algorithm pseudocodes are provided.