论文标题
可计数紧密度和$ C_P $ - 理论的Grothendieck属性
Countable Tightness and the Grothendieck Property in $C_p$-Theory
论文作者
论文摘要
Grothendieck特性在研究病理Banach空间[CI]，[HT]，尤其是[HT20]的确定性方面变得很重要。我们在这里回答了Arhangel'ski \uı的问题，证明了不可确定的lindelöf有限权力是否是Grothendieck。我们通过证明$ \ mathrm {pfa} $意味着Lindelöf的lindelöf很紧张的空间是Grothendieck，我们回答了他的另一个问题。我们还证明，$ \ mathrm {ma} _ {ω_1} $和$ \ mathrm {pfa} $的其他各种后果由Arhangel'ski \uı，Okunev和Reznichenko考虑，不是$ \ Mathrm {Zfc {Zfc} $。
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\uı by proving it undecidable whether countably tight spaces with Lindelöf finite powers are Grothendieck. We answer another of his questions by proving that $\mathrm{PFA}$ implies Lindelöf countably tight spaces are Grothendieck. We also prove that various other consequences of $\mathrm{MA}_{ω_1}$ and $\mathrm{PFA}$ considered by Arhangel'ski\uı, Okunev, and Reznichenko are not theorems of $\mathrm{ZFC}$.
