Geodesic
The Classification of Factors is not Smooth
Canadian journal of mathematics, Tome 25 (1973) no. 1, pp. 96-102

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Woods, E. J. The Classification of Factors is not Smooth. Canadian journal of mathematics, Tome 25 (1973) no. 1, pp. 96-102. doi: 10.4153/CJM-1973-008-7
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