Hausdorf-metric interpretation of convergence in the Matheron topology for binary mathematical morphology

The basic convergence properties of mathematical morphology are characterized in terms of the topology of G. Matheron (1975). That topology is grounded on a particular subbase that can often mask the important metric properties that are consequential to Euclidean morphology. The author presents a development of some of the key Matheron theory in terms of the Hausdorff metric, thereby bypassing the Matheron subbase and giving both theorems and proofs in a metric framework