Contents

# Contents

## Idea

Stably compact spaces are topological spaces which share many of the desirable properties of compact Hausdorff spaces, such as compactness and local compactness, without being Hausdorff or even T1.

They are also a convenient setting for convergence in an ordered setting, being deeply linked to compact ordered spaces.

## Definition

A topological space $X$ is called stably compact if the following conditions are met:

• $X$ is T0;
• $X$ is compact;
• $X$ is locally compact;
• $X$ is sober;
• $X$ is coherent, meaning that the intersection of two compact saturated subsets is compact.

Note that the latter notion of coherence is slightly different than the one given at coherent space.

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## References

Created on October 21, 2019 at 12:59:36. See the history of this page for a list of all contributions to it.