Certain properties of generalized tracially approximated C*-algebras

We show that the following properties of unital ${\mathrm{C}}^{\ast }$-algebra in a class of $\mathrm{\Omega }$ are preserved by unital simple ${\mathrm{C}}^{\ast }$-algebra in the class of $\mathrm{W}\mathrm{T}\mathrm{A}\mathrm{\Omega }$: $(1)$ uniform property $\mathrm{\Gamma }$, $(2)$ a certain type of tracial nuclear dimension at most $n$, $(3)$ weakly $(m,n)$-divisible.