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Hyper-Stonean envelopes of compact spaces

Research output: Contribution to journalJournal article

E-pub ahead of print
<mark>Journal publication date</mark>2019
<mark>Journal</mark>Studia Mathematica
Volume246
Number of pages16
Pages (from-to)31-46
StateE-pub ahead of print
Early online date7/09/18
Original languageEnglish

Abstract

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.