论文标题
产品空间的离散超滤器和同质性
Discrete Ultrafilters and Homogeneity of Product Spaces
论文作者
论文摘要
$ω$上的UltraFilter $ p $如果鉴于任何功能$ f \ colonω\ to x $对于任何完全常规的Hausdorff space，则在p $中有一个$ a \，因此$ f（a）$是离散的。研究了离散超流的基本特性。 $ f $ - 空格之间的三个中间类$ \ MATHSCR R_1 \ subset \ Mathscr R_2 \ subset \ subset \ Mathscr r_3 $在$ f $ spaces的类和van〜douwen的$βΩ$ - 空格的类之间。事实证明，无限紧凑型$ \ Mathscr R_2 $ - 空格的产品是同质的；此外，在假设$ \ mathfrak d = \ mathfrak c $下，没有$βΩ$空间的产品是同质的。
An ultrafilter $p$ on $ω$ is said to be discrete if, given any function $f\colon ω\to X$ to any completely regular Hausdorff space, there is an $A \in p$ such that $f(A)$ is discrete. Basic properties of discrete ultrafilters are studied. Three intermediate classes of spaces $\mathscr R_1 \subset \mathscr R_2 \subset \mathscr R_3$ between the class of $F$-spaces and the class of van~Douwen's $βω$-spaces are introduced. It is proved that no product of infinite compact $\mathscr R_2$-spaces is homogeneous; moreover, under the assumption $\mathfrak d =\mathfrak c$, no product of $βω$-spaces is homogeneous.
