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On the hyperstonean cover of a compact

โœ Scribed by V. K. Zaharov

Publisher
John Wiley and Sons
Year
1982
Tongue
English
Weight
768 KB
Volume
107
Category
Article
ISSN
0025-584X

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โœฆ Synopsis

J. DIXMIER proved i n 1951 ([9]) that any meager set. in Qp is nowhere dense. J. Oxtoby 1)roved in 1961 ([lo]) that p' is regular on&(Q,,), t.hat is for any A mid any E > O tliere exist a closed set F and an open set G such t tint F c r AcG : i t i d /I' (G\F) < F . The space (Q,A. &(Q,). ,A') is called the hyperstonmn space (see [7]. ch. X. $ 3 ) corresponding to tke space (S, X,, p). Lemma. I.. Xerrsaire p' corresponds to a RADON measure on Q,. that is there is n RAINX 1tiects.tcw 1)) o n Q/L m c h that &(Q/() co,iizcirles with the f t r m i l y of crll w -,tiieasuru,bk whscts from 9, and ?jiecr.sure p' coincides with, ~n:': on &i . (Q, , ).

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โœ V. K. Zaharov; A. V. Koldunov ๐Ÿ“‚ Article ๐Ÿ“… 1982 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 657 KB

By Y. K. ZAHAROY and A. 1'. K o r . ~r x o r of Leningrad (R,eceired March 27. 1981) In [ i ] and [2] the notion of u-cover of a compact space was introduced. A compact space a> is called a u -c o w of c( coinpnct spcrce S iff it is the smallest basically disconnected ( = a-extremally disconnected)