Abstract
Abstract In the paper, we introduce a new concept, topological orbit dimension of an n-tuple of elements in a unital C*-algebra. Using this concept, we conclude that Voiculescu's topological free entropy dimension of every finite family of self-adjoint generators of a nuclear C*-algebra is less than or equal to 1. We also show that the Voiculescu's topological free entropy dimension is additive in the full free product of some unital C*-algebras. We show that the unital full free product of Blackadar and Kirchberg's unital MF algebras is also an MF algebra. As an application, we obtain that Ext(C*r (F2) *C C* r (F2)) is not a group.
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