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Hyperfinite type II factor
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, there are up to isomorphism exactly two separably acting <a href="/facts/Von_Neumann_algebra/8NyWUIRH">hyperfinite type II factors</a>; one infinite and one finite. Murray and von Neumann proved that up to <a href="/facts/Isomorphism/pj8KgkxU">isomorphism</a> there is a unique <a href="/facts/Von_Neumann_algebra/8NyWUIRH">von Neumann algebra</a> that is a <a href="/facts/Factor_(functional_analysis)/8NyWUIRH">factor</a> of type II1 and also <a href="/facts/Von_Neumann_algebra/8NyWUIRH">hyperfinite</a>; it is called the hyperfinite type II1 factor. There are an uncountable number of other factors of type II1. <a href="/facts/Alain_Connes/tjFJ9Iou">Connes</a> proved that the infinite one is also unique. </p>