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 thes...
| Authors: | ; ; |
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| Format: | Article |
| Publication date: | 2026 |
| Country: | España |
| Institution: | Universitat Politècnica de València (UPV) |
| Repository: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Language: | English |
| OAI Identifier: | oai:dnet:riunet______::dc39b9faa59b05c6c2efb59e19ba4ae4 |
| Online Access: | https://riunet.upv.es/handle/10251/235476 |
| Access Level: | Open access |
| Keyword: | Cellular-P spaces Cellular-Lindelöf Symmetry g-function Extent DCCC Product Space |
| Summary: | [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. |
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