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Does every non-type-I factor's projection lattice admit a dense embedding of the standard continuum-collapsing poset?
Let $R$ be a non-type-I factor acting on a separable Hilbert space.
Let $P(R)$ be the set of $R$'s projections with the usual ordering ($x \leq y \iff$ range$(x) \subseteq$ range$(y)$) under which it ...
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