О степенных спектрах и композициях финитно строго эпиморфных функторов

The degree spectrum $sp(F)$ of functor $F$ is a set of degrees of points in spaces of the form $F(X)$. We prove that for any subset $K\subset N$ there is strictly epimorphic functor $F$ satisfying certain normality conditions with $sp(F)=K$. We also prove that for strictly epimorphic functor $F$ the composition $F\circ G$ is strictly epimorphic if $sp(F)=N$ and $G$ preserve finite spaces. The composition $G\circ F$ is also strictly epimorphic for any $G$ if $F$ has extension property for finite sections.