Previsions are certain kinds of functionals which model mixtures of probabilistic and non-deterministic choice. For every continuous complete quasimetric X, d, we show that the spaces of (sub)normalized sublinear previsions and of (sub)normalized superlinear previsions on X, with the Kantorovich-Rubinstein quasi-metrics d a KR , are continuous complete. Additionally, the d a KR-Scott topology coincides with the weak topology. If X, d is algebraic complete, then we show that those spaces of previsions are algebraic complete, too, and that finite pointwise suprema (resp., infima) of simple valuations form a strong basis.