A Valdivia compact space with no $G_\delta$ points and few nontrivial convergent sequences

TL;DR

This paper constructs a specific Valdivia compact space lacking $G_\delta$ points and nontrivial convergent sequences outside a dense subset, addressing a problem in Banach space theory.

Contribution

It provides the first example of such a Valdivia compact space with these properties, linking topology and Banach space problems.

Findings

Existence of a Valdivia compact space with no $G_\delta$ points

The space has no nontrivial convergent sequences outside a dense subset

The example relates to twisted sums of Banach spaces

Abstract

We give an example of a Valdivia compact space with no $G_\delta$ points and no nontrivial convergent sequences in the complement of a dense $\Sigma$-subset. The example is related to a problem concerning twisted sums of Banach spaces.