SOME REMARKS ON ALMOST LINDELOF SPACES AND WEAKLY LINDELOF SPACES

A space X is almost Lindelof (weakly Lindelof) if for every open cover u of X, there exists a countable subset V of u such that & Unknown;{(V) over bar : V Epsilon V} = X (respectively, & Unknown; = X). In this paper, we investigate the relationships among almost Lindelof spaces, weakly Lindelof spaces and Lindelof spaces, and also study topological properties of almost Lindelof spaces and weakly Lindelof spaces.