Consider a type $T$, and a set $S$ containing elements of type $T$.
An object $f$ of type $T→T→T$ (or $T^2 → T$) is a function and it is closed under $S$ if any two elements of $S$ applied to $f$ returns an element of $S$. The same goes if $f$ has type $T→T$.
But what if $f$ has type $T$ (i.e., it is a constant, and not a function)? Saying that this $f$ is closed under $S$ is the same as saying that $f$ is an element of $S$?