We propose a family of topologies on the space of consumption patterns in continuous time under uncertainty. Preferences continuous in any of the proposed topologies treat consumptions at nearby dates as almost perfect substitutes except possibly at information surprises. The topological duals of the family of proposed topologies essentially contain processes that are the sums of processes of absolutely continuous paths and martingales. Thus if equilibrium prices for consumption come from the duals, consumptions at nearly adjacent dates in a state of nature have almost equal prices except possibly at information surprises. In particular, if the information structure is generated by a Brownian motion, the duals are composed of Ito processes. We investigate some implications of our topologies on standard models of choice in continuous time as well as on recent models of non-time-separable representations of preferences. We also discuss the properties of prices of long-lived assets in economies populated with agents whose preferences are continuous in our topologies when there are no arbitrage opportunities.