T_0 functional Alexandroff topologies are partial metrizable
[EN] If f : X → X is a function, the associated functional Alexandroff topology on X is the topology whose closed sets are {A ⊆ X : f(A) ⊆ A}. We prove that every functional Alexandroff topology is pseudopartial metrizable and every T0 functional Alexandroff topology is partial metrizable.
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/210129 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/210129 |
| Access Level: | acceso abierto |
| Palabra clave: | Functional Alexandroff topology Partial metric Pseudopartial metric |
| Sumario: | [EN] If f : X → X is a function, the associated functional Alexandroff topology on X is the topology whose closed sets are {A ⊆ X : f(A) ⊆ A}. We prove that every functional Alexandroff topology is pseudopartial metrizable and every T0 functional Alexandroff topology is partial metrizable. |
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