论文标题
批次在功能上可数的对角线的补充是什么时候？
When is the complement of the diagonal of a LOTS functionally countable?
论文作者
论文摘要
在2021年的论文中，Vladimir Tkachuk询问是否有一个不可分割的批次$ x $，以至于$ x^2 \ setMinus \ {\ langle x，x \ rangle \ rangle \ colon x \ in x \} $是功能上可计数的。在本文中，我们证明，如果存在这样的空间，则必须是Aronszajn线，并承认$ \ leq 2 $ -to- $ 1 $ 1 $ 1 $ 1 $回收到Suslin Line的子空间。在此之后，假设存在SUSLIN线，我们证明存在功能上可计数的SUSLIN线。最后，我们提供了一个在功能上可计数的suslin行$ l $的示例，以便$ l^2 \ setMinus \ {\ langle x，x \ rangle \ colon x \ in L \} $在功能上不可数。
In a 2021 paper, Vladimir Tkachuk asked whether there is a non-separable LOTS $X$ such that $X^2\setminus\{\langle x,x\rangle\colon x\in X\}$ is functionally countable. In this paper we prove that such a space, if it exists, must be an Aronszajn line and admits a $\leq 2$-to-$1$ retraction to a subspace that is a Suslin line. After this, assuming the existence of a Suslin line, we prove that there is Suslin line that is functionally countable. Finally, we present an example of a functionally countable Suslin line $L$ such that $L^2\setminus\{\langle x,x\rangle\colon x\in L\}$ is not functionally countable.
