{V : V ∈ Vn} = X . Clearly, every Menger space is almost Menger and every almost Menger space is weakly Menger, but the converses do not hold (see Examples 2.1 and 2.2). On the study of weakly Menger spaces, almost Menger spaces and Menger spaces, the readers can see the references [2, 3, 4, 5, 6]. Here we investigate the relationships among almost Menger spaces, weakly Menger spaces and Menger...