  We consider general non-Euclidean distance measures between real world
objects that need to be classified. It is assumed that objects are represented
by distances to other objects only. Conditions for zero-error dissimilarity
based classifiers are derived. Additional conditions are given under which the
zero-error decision boundary is a continues function of the distances to a
finite set of training samples. These conditions affect the objects as well as
the distance measure used. It is argued that they can be met in practice.
