How Do Domains Model Topologies?

AbstractIn this brief study we explicitly match the properties of spaces modelled by domains with the structure of their models. We claim that each property of the modelled topology is coupled with some construct in the model. Examples are pairs: (i) first-countability - strictly monotone map, (ii) developability - measurement, (iii) metrizability - partial metric, (iv) ultrametrizability - tree, (v) Choquet-completeness - dcpo, and more. By making this correspondence precise and explicit we reveal how domains model topologies