Covering Dimension for Nuclear C * -algebras

  title={Covering Dimension for Nuclear C * -algebras},
  author={Wilhelm Winter},
We introduce the completely positive rank, a notion of covering dimension for nuclear C *-algebras and analyze some of its properties. The completely positive rank behaves nicely with respect to direct sums, quotients, ideals and inductive limits. For abelian C *-algebras it coincides with covering dimension of the spectrum and there are similar results for continuous trace algebras. As it turns out, a C *-algebra is zero-dimensional precisely if it is AF. We consider various examples… CONTINUE READING
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