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Dominance diagrams are an extension of the conceptual neighbourhood diagrams (CNDs) that have become familiar in the areas of qualitative spatial and temporal knowledge representation. They are also related to the envisionment diagrams of qualitative physics. This paper explains the concept of dominance between qualitative states and shows how, by adding a representation of this relation to CNDs, it is possible to reason more effectively about the temporal incidence of the qualitative states represented in the diagrams; in addition, dominance turns out to be of importance in determining the structure of composite diagrams formed as the product of existing diagrams. It is further shown that the appropriate theoretical underpinning for dominance diagrams is the mathematical theory of T0 topological spaces.