Before revision:  As a byproduct of our isometry theorem, we prove that the convolution distance is closed, and also give c}(}\textbf{  some explicit examples of computation of the convolution distance.
After revision:  As a byproduct of our isometry theorem, we prove that the convolution distance is closed, give a precise description of connected components of D^b_{\mathbb{R c}(}\textbf{ some explicit examples of computation of the convolution distance.