Models improved

A model of a space X is a dcpo Y whose subspace of maximal elements is isomorphic to X. Of particular importance are those spaces that have ω-continuous models. This topic is covered in Section 7.7.2 of the book. Martin [3], and Mummert and Stephan [1] came very close to characterize them exactly. See the full post.

Quasi-polish spaces

Polish spaces are an important class of spaces.  I am dealing with them in Section 7.7 of the book. But they are Hausdorff spaces, and the purpose of the book was to explore non-Hausdorff spaces. Matthew de Brecht found a non-Hausdorff generalization of Polish spaces, which he aptly called quasi-Polish spaces. See the full post.