Complete exhaustive sieves and games

Properties of completely regular spaces with complete exhaustive sieves are studied using the equivalent notion of partition complete spaces and associated games. Among others the following results are proved. (1) If $X$ is the intersection of countably many partition complete subsets of $Y$, then $X$ is partition complete. (2) If $X$ is $K$-scattered, where $K$ is the class of all partition complete spaces, then $X$ is partition complete. (3) If $X$ is a primitive set in a $C$-scattered space $Y$, then $X$ is the intersection of countably many $C$-scattered subsets of $Y$. (4) The partition completeness is perfect and preserved by open maps.