Definition:Compact Locale

Definition

Let $L = \struct{S, \preceq}$ be a locale with greatest element $\top$.

Then:

$L$ is said to be a compact locale if and only if $\top$ is a compact element.

Also see

• Characterization of Compact Element in Frame or Locale

Sources

• 1982: Peter T. Johnstone: Stone Spaces: Chapter $\text {III}$: Compact Hausdorff Spaces, $\S1.1$