Separated Lattices of Multiply $ \sigma $-Local Formations

Let $ n>0 $ and let $ \sigma=\{\sigma_{i}\mid i\in I\} $ be a partition of the set of all primes $ {𝕇} $ . We prove that the lattice of all $ n $ -multiply $ \sigma $ -local formations is inductive and $ {\mathfrak{G}} $ -separated.