O'Reilly logo

Non-Hausdorff Topology and Domain Theory by Jean Goubault-Larrecq

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

9

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 image is stably compact. More generally, every finite ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required