Nonincrease of Density and Weak Density under Weakly Normal Functors

In this paper, it is proved that if a covariant functor $\mathscr F\colon\mathrm{Comp}\to\mathrm{Comp}$ is weakly normal, then $d(\mathscr F^\beta(X))\le d(X)$ and $wd(\mathscr F^\beta(X))\le wd(X)$ for any infinite Tychonoff space $X$.