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Hyper-Stonean envelopes of compact spaces

Research output: Contribution to journalJournal articlepeer-review

<mark>Journal publication date</mark>2019
<mark>Journal</mark>Studia Mathematica
Number of pages16
Pages (from-to)31-46
Publication StatusPublished
Early online date7/09/18
<mark>Original language</mark>English


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