论文标题
在$ n $饱和的闭合图上
On $n$-saturated closed graphs
论文作者
论文摘要
Geschke证明了$ 2^ω$上有3个饱和的clopen图，但是$ 2^ω$上的clopen图甚至没有4饱和的无限子图；但是，有$f_σ$图是$ω_1$ - 饱和。事实证明，$ 2^ω$（即$ω$）上没有封闭图。在本说明中，我们通过证明每$ n $都有$ n $饱和的封闭图$ 2^ω$来完成这张图片。关键引理基于概率论点。最终构造是有限图的反度。
Geschke proved that there is clopen graph on $2^ω$ which is 3-saturated, but the clopen graphs on $2^ω$ do not even have infinite subgraphs that are 4-saturated; however there is $F_σ$ graph that is $ω_1$-saturated. It turns out that there is no closed graph on $2^ω$ which is $ω$-saturated. In this note we complete this picture by proving that for every $n$ there is an $n$-saturated closed graph on the Cantor space $2^ω$. The key lemma is based on probabilistic argument. The final construction is an inverse limit of finite graphs.
