Countable Tightness and the Grothendieck Property in $C_p$-Theory
General Topology
2020-07-20 v1
Abstract
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 Arhangel'ski\u{\i} by proving it undecidable whether countably tight spaces with Lindel\"of finite powers are Grothendieck. We answer another of his questions by proving that implies Lindel\"of countably tight spaces are Grothendieck. We also prove that various other consequences of and considered by Arhangel'ski\u{\i}, Okunev, and Reznichenko are not theorems of .
Keywords
Cite
@article{arxiv.2007.08579,
title = {Countable Tightness and the Grothendieck Property in $C_p$-Theory},
author = {Franklin D. Tall},
journal= {arXiv preprint arXiv:2007.08579},
year = {2020}
}