Countable Tightness and the Grothendieck Property in $C_p$-Theory

DOI10.1016/J.TOPOL.2022.108299arXiv2007.08579MaRDI QIDQ6345252

Publication date: 16 July 2020

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'skiu{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

m a t h r m P F A

implies Lindel"of countably tight spaces are Grothendieck. We also prove that various other consequences of

m a t h r m {M A}_{o m e g a_{1}}

and

m a t h r m P F A

considered by Arhangel'skiu{i}, Okunev, and Reznichenko are not theorems of

m a t h r m Z F C

.

Mathematics Subject Classification ID

Function spaces in general topology (54C35) Cardinality properties (cardinal functions and inequalities, discrete subsets) (54A25) Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) (54A20) Counterexamples in general topology (54G20) Consistency and independence results in general topology (54A35)

This page was built for publication: Countable Tightness and the Grothendieck Property in $C_p$-Theory

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6345252)