Sub-Stonean space

In topology, a sub-Stonean space is a locally compact Hausdorff space such that any two open σ-compact disjoint subsets have disjoint compact closures. Related, an F-space, introduced by Gillman & Henriksen (1956), is a completely regular Hausdorff space for which every finitely generated ideal of the ring of real-valued continuous functions is principal, or equivalently every real-valued continuous function ${\displaystyle f}$ can be written as ${\displaystyle f=g|f|}$ for some real-valued continuous function ${\displaystyle g}$. When dealing with compact spaces, the two concepts are the same, but in general, the concepts are different. The relationship between the sub-Stonean spaces and F-spaces is studied in Henriksen and Woods, 1989.