Sub-Stonean space
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In topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...

, a sub-Stonean space (or F-space) is a locally compact Hausdorff space
Hausdorff space
In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space in which distinct points have disjoint neighbourhoods. Of the many separation axioms that can be imposed on a topological space, the "Hausdorff condition" is the most frequently...

 such that any two open σ-compact disjoint subsets have disjoint compact closures. They were introduced by

Rickart space
Rickart space
In mathematics, a Rickart space , also called a basically disconnected space, is a topological space in which open σ-compact subsets have compact open closures...

s and the corona set
Corona set
In mathematics, the corona or corona set of a topological space X is the complement βX\X of the space in its Stone–Čech compactification βX....

s of locally compact σ-compact Hausdorff spaces are sub-Stonean spaces.
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