Additional set-theoretic assumptions and twisted sums of Banach spaces

TL;DR

This paper explores how extra set-theoretic assumptions influence the existence of nontrivial twisted sums involving the Banach space c_0 and continuous function spaces on nonmetrizable compact spaces.

Contribution

It investigates the impact of set-theoretic assumptions on the existence of twisted sums of Banach spaces, focusing on c_0 and nonmetrizable compact spaces.

Findings

Set-theoretic assumptions affect twisted sum existence.

Conditions for nontrivial twisted sums are characterized.

Results connect set theory with Banach space structure.

Abstract

In this paper, we discuss the role played by additional set-theoretic assumptions in the investigation of the existence of nontrivial twisted sums of $c_0$ and spaces of continuous functions on nonmetrizable compact Hausdorff spaces.