Some remarks on generalizations of countably compact spaces and Lindelöf spaces

On relatively almost countably compact subsets

“…Let us recall that a space X is countably compact if every countable open cover of X has a finite subcover. As a generalization of countable compactness, Bonanzinga, Matveev and Pareek [1] defined a space X to be almost countably compact if for every countable open cover U of X there exists a finite subset V of U such that {V : V ∈ V } = X. Clearly, every countably compact space is almost countably compact.…”