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Do people really use such an unlovely adjective? Distinguishing between “Stone locales” and “Stonean locales” seems like a recipe for lots of confusion to me.
This terminology dates back at least to Dixmier’s 1951 classical paper on hyperstonean spaces (available on my website). He uses “espace stonien” and “espace hyperstonien” for Stonean respectively hyperstonean spaces.
Takesaki in his book (Theory of Operator Algebras) also uses it.
I don’t know of a better name and this one seems to be recognized in the literature. (The definition is indeed due to M. H. Stone, see his 1937 paper.)
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