On \v{C}ech-completeness of the space of order-preserving functionals

TL;DR

This paper proves that the ch-completeness property of a Tychonoff space X is preserved in the space of ch-complete order-preserving, weakly additive, normed functionals on X, expanding understanding of functional space properties.

Contribution

It establishes that ch-completeness is maintained in the space of ch-complete order-preserving functionals, a novel result linking space completeness with functional space structure.

Findings

ch-completeness of X implies ch-completeness of O_(X)

The space of ch-complete order-preserving functionals inherits completeness

The result applies to Tychonoff spaces with ch-completeness property.

Abstract

In this paper we establish that if a Tychonoff space $X$ is \v{C}ech-complete then the space $O_\tau(X)$ of all $\tau$-smooth order-preserving, weakly additive and normed functionals is also \v{C}ech-complete