Countable tightness is not discretely reflexive in $σ$-compact spaces

István Juhász, Jan van Mill

Published 2024-11-07Version 1

Answering a question raised by V. V. Tkachuk, we present several examples of $\sigma$-compact spaces, some only consistent and some in ZFC, that are not countably tight but in which the closure of any discrete subset is countably tight. In fact, in some of our examples the closures of all discrete subsets are even first countable.