T_0 functional Alexandroff topologies are partial metrizable
Submitted: 2023-03-19
|Accepted: 2023-09-19
|Published: 2024-10-01
Copyright (c) 2024 Homeira Pajoohesh
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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Keywords:
functional Alexandroff topology, partial metric, pseudopartial metric
Supporting agencies:
Abstract:
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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