Sammendrag
We investigate domains with totality where density in general does not hold. We define three categories of domains with totality satisfying certain structural properties. These will induce domains with totality. We show that the category of evaluation structures is closed under dependent sums and products, under a universe constructor and under direct limits. This is applied to domains with totality defined by induction. We also investigate the topological properties of domains with totality induced from evaluation structures.