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

TL;DR

This paper proves that certain functors related to order-preserving functionals preserve the weight and do not increase the density of infinite Tychonoff spaces, contributing to the understanding of their topological properties.

Contribution

It establishes that the functors $O_ au$ and $O_R$ preserve weight and do not increase density or weak density of infinite Tychonoff spaces.

Findings

Functors $O_ au$ and $O_R$ preserve the weight of spaces.

Density and weak density do not increase under these functors.

Results apply to infinite Tychonoff spaces.

Abstract

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.