The Classification of Factors is not Smooth
1973 ◽
Vol 25
(1)
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pp. 96-102
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Keyword(s):
There is a natural Borel structure on the set F of all factors on a separable Hilbert space [3]. Let denote the algebraic isomorphism classes in F together with the quotient Borel structure. Now that various non-denumerable families of mutually non-isomorphic factors are known to exist [1; 6; 8; 10; 11; 12; 13], the most obvious question to be resolved is whether or not is smooth (i.e. is there a countable family of Borel sets which separate points). We answer this question negatively by an explicit construction.
2004 ◽
Vol 56
(4)
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pp. 742-775
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Keyword(s):
1982 ◽
Vol 34
(6)
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pp. 1245-1250
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Keyword(s):