Order preserving quotient lifting properties

TL;DR

This paper introduces order preserving quotient lifting and compact lifting properties, demonstrating the compact quotient lifting property for affine continuous functions on a Choquet simplex and those vanishing on a metrizable face.

Contribution

It formulates new lifting properties in the context of affine continuous functions and establishes their validity for specific spaces related to Choquet simplices.

Findings

Established the compact quotient lifting property for affine continuous functions on Choquet simplices.

Proved the property for functions vanishing on a metrizable face.

Extended the understanding of lifting properties in functional analysis.

Abstract

In this paper we formulate order preserving quotient lifting property and the compact lifting property. In the case of affine continuous functions on a Choquet simplex, we show the compact quotient lifting property for the space of affine continuous functions and those vanishing on a metrizable face.