Not OCA and products of Frechet spaces

TL;DR

This paper explores whether the product of two countable Fréchet spaces is M-separable, focusing on the influence of Martin's Axiom and showing that OCA implies an affirmative answer.

Contribution

It investigates the independence of the M-separability of products of countable Fréchet spaces from Martin's Axiom, highlighting the role of OCA in this context.

Findings

OCA implies the product of two countable Fréchet spaces is M-separable.

The question is independent of Martin's Axiom in models where c ≤ ω₂.

The paper advances understanding of topological properties under set-theoretic assumptions.

Abstract

We continue the investigation of the question of whether the product of two countable Fr\'echet spaces must be M-separable. We are especially interested in this question in the presence of Martin's Axiom. The question has been shown to be independent of Martin's Axiom but only in models in which $\mathfrak c\leq\omega_2$. In fact, OCA implies an affirmative answer.