A Moore space with a 𝜎-discrete 𝜋-base which cannot be densely embedded in any Moore space with the Baire property

Abstract

The author answers a question raised in the literature about twenty five years ago and raised again more recently in Open Problems in Topology, by G. M. Reed, concerning the conjecture that every Moore space with a σ \sigma -discrete π \pi -base can be densely embedded in a Moore space having the Baire property. Even though closely related results have made this conjecture seem likely to be true, the author shows that, surprisingly, the conjecture is false.