Bounded complete models of topological spaces
This paper provides a positive solution to a question of the reviewer and generalizes earlier related results by establishing that a metrizable space is completely metrizable if and only if it can be embedded as the set of maximal points of a bounded complete continuous domain (equipped with the relative Scott topology). The proof establishes and then exploits a generalization of the fact that a completely metrizable space \((X,\tau)\) admits a compact \(T_1\)-topology \(\tau^*\subseteq \tau\) such that the bitopological space \((X,\tau,\tau^*)\) is completely regular.
scientific article; zbMATH DE number 2092805