Stably compact spaces and compact pospaces
9.1 Stably locally compact spaces, stably compact spaces
We have already introduced the notion of stably locally compact space in Definition 8.3.31. A stably compact space is only moderately more constrained:
Definition 9.1.1 (Stably compact space) A topological space is stably compact if and only if it is stably locally compact and compact.
In other words, a space is stably compact if and only if it is sober, locally compact, compact, and coherent; alternatively, if and only if it is T0, well-filtered, locally compact, compact, and coherent.
Example 9.1.2 is stably compact. More generally, every finite ...