Nontrivial twisted sums for finite height spaces under Martin's Axiom

TL;DR

Under Martin's Axiom, the paper proves the existence of nontrivial twisted sums of c_0 and C(K) for all finite height compact spaces K with sufficiently large weight, resolving an open problem.

Contribution

The paper establishes the existence of nontrivial twisted sums for a broad class of finite height spaces under Martin's Axiom, filling a key gap in the theory.

Findings

Existence of nontrivial twisted sums under Martin's Axiom

Applicable to all finite height compact spaces with large weight

Resolves an open problem in the field

Abstract

We show that if we assume Martin's Axiom, then there exists a nontrivial twisted sum of c_0 and C(K), for every compact space K with finite height and weight at least continuum. This result settles the problem of existence of nontrivial twisted sums of c_0 and C(K), for finite height spaces K, under Martin's Axiom.