Stable Neighborhoods

Abstract

Scott topology plays an essential role for the logic of domains developed in Part I. One of the reasons for this is that Scott open sets characterize continuous functions. Scott open sets on stable domains, however, do not characterize stable functions. They do not characterize the stable order, in particular. This makes key rules like

$$ \frac{{A \le A'\quad B' \le B}}{{A' \to B' \le A \to B}}$$

inappropriate for the stable case.