论文标题
关于泰乔诺夫空间中投影集的减少和分离
On reduction and separation of projective sets in Tychonoff spaces
论文作者
论文摘要
我们表明，对于每个Tychonoff空间$ x $和HAUSDORFF操作$ \MATHBFφ$，$ \MATHBFφ类（\ Mathscr z，x）$从零套装中产生的$ x $ by $ x $ byMathbfφ$具有降低或分离属性，如果相应的$ \ nathbfc也相同\ nathbf；特别是，在投影性的决定性下，这些投影集中的这些属性$ x $具有与第一个周期性定理的模式相同的模式，用于投影的真实集合：$ \mathbfς^{1} _ {2n} _ {2n} _ {2n}（\ Mathscr z，x）还原属性时，$ \MATHBFπ^{1} _ {2n}（\ Mathscr Z，X）$和$ \MathBfς^{1} _ {2n+1}（\ Mathscr Z，X）$具有分离属性。
We show that for every Tychonoff space $X$ and Hausdorff operation $\mathbfΦ$, the class $\mathbfΦ(\mathscr Z,X)$ generated from zero sets in $X$ by $\mathbfΦ$ has the reduction or separation property if the corresponding class $\mathbfΦ(\mathscr F,\mathbb R)$ of sets of reals has the same property. In particular, under Projective Determinacy, these properties of such projective sets in $X$ have the same pattern as the First Periodicity Theorem states for projective sets of reals: the classes $\mathbfΣ^{1}_{2n}(\mathscr Z,X)$ and $\mathbfΠ^{1}_{2n+1}(\mathscr Z,X)$ have the reduction property while $\mathbfΠ^{1}_{2n}(\mathscr Z,X)$ and $\mathbfΣ^{1}_{2n+1}(\mathscr Z,X)$ have the separation property.
