Pervasive and weakly pervasive pre-Riesz spaces

TL;DR

This paper introduces intrinsic characterizations of pervasive and weakly pervasive pre-Riesz spaces, simplifying their identification and exploring their relation to the Riesz decomposition property.

Contribution

It provides new intrinsic criteria for pervasive pre-Riesz spaces and introduces the concept of weakly pervasive pre-Riesz spaces, facilitating easier analysis.

Findings

Intrinsic characterizations of pervasive pre-Riesz spaces

Introduction of weakly pervasive pre-Riesz spaces

Relation to pre-Riesz spaces with Riesz decomposition property

Abstract

Pervasive pre-Riesz spaces are defined by means of vector lattice covers. To avoid the computation of a vector lattice cover, we give two distinct intrinsic characterizations of pervasive pre-Riesz spaces. We introduce weakly pervasive pre-Riesz spaces and observe that this property can be easily checked in examples. We relate weakly pervasive pre-Riesz spaces to pre-Riesz spaces with the Riesz decomposition property.