A note on fragmentability and weak-G_delta sets

TL;DR

This paper introduces a new class of Banach spaces characterized by their fragmentability properties, specifically spaces that lack weak-G_delta open bounded subsets, highlighting a distinction from separable polyhedral spaces.

Contribution

It defines a novel class of Banach spaces based on fragmentability, showing they do not contain weak-G_delta open bounded subsets and are not isomorphic to separable polyhedral spaces.

Findings

Identified a new class of Banach spaces with specific fragmentability properties.

Proved these spaces do not contain weak-G_delta open bounded subsets.

Established these spaces are not isomorphic to separable polyhedral spaces.

Abstract

In terms of fragmentability, we describe a new class of Banach spaces which do not contain weak-G_delta open bounded subsets. In particular, none of these spaces is isomorphic to a separable polyhedral space.