Hyper-stonean Envelopes of Compact Spaces
نویسنده
چکیده
Let K be a compact space, and denote by K̃ its hyperStonean envelope. We discuss the class of spaces K with the property that K̃ is homeomorphic to Ĩ, the hyper-Stonean envelope of the closed unit interval I. Certainly each uncountable, compact, metrizable space K belongs to this class. We describe several further classes of compact spaces K for which K̃ = Ĩ. In fact, K̃ = Ĩ if and only if the Banach spaces M(K) and M(I) of measures on K and I are isometrically isomorphic.
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