  In the paper, we introduce a new concept of topological orbit dimension of
$n$-tuples of elements in a unital C$^*$ algebra. Using this concept, we
conclude that the Voiculescu's topological free entropy dimension of any family
of self-adjoint generators of a nuclear C$^*$ algebra is less than or equal to
1. We also show that the topological free entropy dimension is additive in the
full free products of unital C$^*$ algebras. In the appendix, we show that
unital full free product of Blackadar and Kirchberg's unital MF algebras is
also MF algebra.
