A note on spaces that are finitely an F-space

A Tychonoff space X is finitely an F-space if βX is expressible as a union of finitely many closed F-spaces. Larson [13] has shown that, for normal spaces X, the property of being finitely an F  -space can be characterized in terms of algebraic properties of the ring C(X)C(X). By extending this notion to locales, we show that the normality restriction can actually be dropped, even in spaces, and thus sharpen Larson's result.