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Hyper-Stonean envelopes of compact spaces

Research output: Contribution to journalJournal article

<mark>Journal publication date</mark>13/02/2018
<mark>Journal</mark>Studia Mathematica
Number of pages18
<mark>State</mark>Accepted/In press
<mark>Original language</mark>English


Let K be a compact space, and denote by eK its hyper-Stonean envelope. We discuss the class of spaces K with the property that eK is homeomorphic toe I, 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 eK =e I. In fact, eK =eI if and only if the Banach spaces M(K) and M(I) of measures on K and I are isometrically isomorphic.