On the weight and the density of the space of order-preserving functionals

In the present paper it is proved that the functors $O_{\tau }$ of $\tau$-smooth order preserving functionals and $O_R$ of Radon order preserving functionals preserve the weight of infinite Tychonoff spaces. Moreover, it is established that the density and the weak density of infinite Tychonoff spaces do not increase under these functors.