论文标题
$ q $ - 空间，完美的空间和连续体的基本特征
$Q$-spaces, perfect spaces and related cardinal characteristics of the continuum
论文作者
论文摘要
如果$ x $的每个子集都是$ x $中的$ x $，则拓扑空间$ x $称为$ q $ -space。对于$ i \ in \ {1,2,3 \} $，让$ \ mathfrak q_i $是第二个可容纳$ t_i $ -space的最小基数，这不是$ q $ -space。显然，$ \ Mathfrak Q_1 \ Le \ Mathfrak Q_2 \ Le \ Mathfrak Q_3 $。对于$ i \ in \ {1,2 \} $，我们证明$ \ mathfrak q_i $等于不完美的第二个可算出$ t_i $ -space的最小基数。另外，我们证明$ \ Mathfrak Q_3 $等于可分离空间的最小基数，这不是$ q $ -space。马丁的公理意味着$ \ mathfrak q_i = \ mathfrak c $ for All $ i \ in \ in \ {1,2,3 \} $。
A topological space $X$ is called a $Q$-space if every subset of $X$ is of type $F_σ$ in $X$. For $i\in\{1,2,3\}$ let $\mathfrak q_i$ be the smallest cardinality of a second-countable $T_i$-space which is not a $Q$-space. It is clear that $\mathfrak q_1\le\mathfrak q_2\le\mathfrak q_3$. For $i\in\{1,2\}$ we prove that $\mathfrak q_i$ is equal to the smallest cardinality of a second-countable $T_i$-space which is not perfect. Also we prove that $\mathfrak q_3$ is equal to the smallest cardinality of a submetrizable space, which is not a $Q$-space. Martin's Axiom implies that $\mathfrak q_i=\mathfrak c$ for all $i\in\{1,2,3\}$.
