Large weight does not yield an irreducible base

TL;DR

This paper demonstrates that it is consistent for certain first countable spaces with uncountable weight to lack uncountable subspaces with an irreducible base, addressing a question in topology.

Contribution

It provides a consistency result showing the existence of such spaces, answering an open question in the field.

Findings

First countable spaces of uncountable weight may lack uncountable subspaces with irreducible bases

Addresses a question posed by Juhasz, Soukup, and Szentmiklossy

Establishes a new consistency result in topology

Abstract

Answering a question of Juhasz, Soukup and Szentmikl\'ossy we show that it is consistent that some first countable space of uncountable weight does not contain an uncountable subspace which has an irreducible base.