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Recently I asked the following question, about the separability of the underlying $C^*$-algebra in the definition of $K$-homology:

mathoverflow.net/questions/181361

As far as I understood, in order to have well behaved theory (functoriality, six term exact sequence etc) we have to assume that our $C^*$-algebra is separable. This is in contrast with $K$-theory. Some time ago I asked also the following, natural question:

mathoverflow.net/questions/169270/

So the natural continuation of those topics would be the following:

Question: which groups may be obtained as $K$-homology groups for a separable $C^*$-algebra?

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  • $\begingroup$ For C* algebras in the bootstrapclass it can be calculated using the universal coefficient theorem. Then one can observe for example that the K-homology of separable c*algebras can be uncountable.. $\endgroup$
    – Sabrina Gemsa
    Commented Apr 24, 2017 at 2:37

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