9 citations · 44 across the 28 of their papers we have counts for
18 papers · 1 filter
Countable Tightness and the Grothendieck Property in -Theory
Franklin D. Tall
The Grothendieck property has become important in research on the definability of pathological Banach spaces [CI], [HT], and especially [HT20]. We here answer a question of Arhange…
The Strength of Menger's Conjecture
Franklin D. Tall, Stevo Todorcevic, Seçil Tokgöz
Menger conjectured that subsets of R with the Menger property must be -compact. While this is false when there is no restriction on the subsets of R, for projective subsets it i…
Completely Baire spaces, Menger spaces, and projective sets
Franklin D. Tall, Lyubomyr Zdomskyy
W. Hurewicz proved that analytic Menger sets of reals are -compact and that co-analytic completely Baire sets of reals are completely metrizable. It is natural to try to general…
Definable versions of Menger's conjecture
Franklin D. Tall
Menger's conjecture that Menger spaces are /sigma-compact is false; it is true for analytic subspaces of Polish spaces and undecidable for more complex definable subspaces of Polis…
Hereditarily normal manifolds of dimension > 1 may all be metrizable
Alan Dow, Franklin D. Tall
P.J. Nyikos has asked whether it is consistent that every hereditarily normal manifold of dimension > 1 is metrizable, and proved it is if one assumes the consistency of a supercom…
On the definability of Menger spaces which are not /sigma-compact
Franklin D. Tall, Secil Tokgoz
Hurewicz proved completely metrizable Menger spaces are /sigma-compact. We extend this to Cech-complete Menger spaces and consistently to projective Menger metrizable spaces. On th…