A note on weakly Lindelof frames

The notion of sigma-properness of a subset of a frame is introduced. Using this notion, we give necessary and sucient conditions for a frame to be weakly Lindelof. We show that a frame is weakly Lindelof if and only if its semiregularization is weakly Lindelof. For a completely regular frame L, we introduce a condition equivalent to weak realcompactness based on maximal ideals of the cozero part of L. This enables us to show that every weakly realcompact almost P -frame is realcompact. A new characterization of weakly Lindelof frames in terms of neighbourhood strongly divisible ideals of ?? is provided. The closed ideals of ?? equipped with the uniform topology are applied to describe weakly Lindelof frames.