Some results on the $\pi$-weight of countable Fr\'echet-Urysohn spaces

TL;DR

This paper investigates the possible sizes of the $\pi$-weight spectrum in countable regular Fréchet-Urysohn spaces, determining it within specific set-theoretic models, thus linking topology with set theory.

Contribution

It characterizes the $\pi$-weight spectrum of countable regular Fréchet-Urysohn spaces in the Miller and Random real models, providing new insights into their set-theoretic properties.

Findings

The $\pi$-weight spectrum is explicitly determined in the Miller model.

The $\pi$-weight spectrum is explicitly determined in the Random real model.

Results connect topological properties with set-theoretic assumptions.

Abstract

The $\pi$-weight spectrum for countable regular Fr\'echet-Urysohn spaces is the set of uncountable cardinals that are equal to the $\pi$-weight for some such space. We determine this $\pi$-weight spectrum in the standard Miller rational perfect set model and in the Random real model.