Update: Remarks on Countable Tightness

TL;DR

This paper provides a complete alternative proof for a key lemma in a 2014 topology paper, addressing previous shortcomings and ensuring the validity of the original theorem on countable tightness.

Contribution

It offers a corrected, detailed proof of Lemma 10 from Scheepers' 2014 work, strengthening the original results on countable tightness.

Findings

The original proof of Lemma 10 had gaps.

The new proof resolves previous shortcomings.

Theorem 11's validity is now fully supported.

Abstract

The proof of Theorem 11 of the paper M. Scheepers, Remarks on countable tightness, Topology and its Applications 161 (2014), 407 - 432 relies on Lemma 10 of that paper. The offered proof of Lemma 10 had shortcomings, and I was recently asked for details. This note gives an alternative, complete proof of Lemma 10.