T_0 functional Alexandroff topologies are partial metrizable

• Pajoohesh, Homeira ^[1]
  1. [1] Medgar Evers College

     Medgar Evers College

     Estados Unidos

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 25, Nº. 2, 2024, págs. 305-319
• Idioma: inglés
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• Resumen

  • 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.