Cellular-P spaces for some Lindelöf-type properties

[EN] In this paper, we study two classes of topological spaces: cellular-almost Lindelöf spaces and cellular-weakly Lindelöf spaces. We prove that the classes of cellular-Lindelöf, cellular weakly Lindelöf and cellular-almost Lindelöf are distinct. In addition, we present a comparative study of these classes. We also establish some cardinality results. In particular, we prove that, under the assumption of 2<c =c , every normal first-countable sequential cellular-weakly Lindelöf space has cardinality at most the continuum. This result generalizes a result by Bella and Spadaro. Furthermore, we prove that if a space X is normal, satisfies the DCCC property, possesses a symmetric g-function g with the property that ? { g ( ( n , x ) ) : n ? ? } = { x } for each x ? X and H ? ( X ) = ? , then its cardinality is bounded by c.