Cellular-P spaces for some Lindelöf-type properties
Submitted: 2025-08-27
|Accepted: 2026-04-03
|Published: 2026-05-27
Copyright (c) 2026 Iván Martínez-Ruiz, Cesar Alonzo Moreno-Espinoza, Alejandro Ramírez Páramo
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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Keywords:
cellular-P spaces, cellular-Lindelöf, symmetry g-function, extent, DCCC, Product Space
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Abstract:
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 ∈ ω } = { x } for each x ∈ X and H ψ ( X ) = ω , then its cardinality is bounded by c.
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