In the paper Edge analysis and identification using the continous shearlet transform (by K. Guo, D. Labate and W. Lim) I encountered the term smooth partition of a set. I do not understand the term smooth partition Lets be precise what is written:
[...]let $\Omega$ be a bounded open subset of $R^2$ and assume a smooth partition $\Omega=\cup_n(\Omega_n \cup \Gamma)$, where [...]
now there are severel requirements listed. To be clear, I know what a partition is, but I only know the term smooth in the sense of a smooth function. Thanking you in anticipation.