On certain properties of the spaces of order-preserving functionals

In the present paper it is proved that the functor O τ of τ-smooth order preserving functionals and the functor O R of Radon order preserving functionals, do not change the weight of infinite Tychonoff spaces. It is shown that the density and the weak density of infinite Tychonoff spaces do not increase under these functors. Moreover, if X is a metric space with the second axiom of countability then the spaces O τ ( X ) and O R ( X ) are also metrizable.