论文标题
在范围断开范围的一组指标上
On comeager sets of metrics whose ranges are disconnected
论文作者
论文摘要
对于一个可Metrizable的空间$ x $，我们用$ \ mathrm {metrm {met}（x）$表示所有产生$ x $的拓扑的公制空间。 Space $ \ Mathrm {Met}（X）$配备了超级距离。在本文中，对于每一个强大的零维度可衡量空间$ x $，我们证明其范围封闭的所有指标集完全断开了该行的连接子集，这是一个密集的$g_Δ$子空间，in $ \ mathrm {metrm {met}（x）（x）$。作为应用程序，我们表明，在指标空间中，一些通用指标集很小。
For a metrizable space $X$, we denote by $\mathrm{Met}(X)$ the space of all metric that generate the same topology of $X$. The space $\mathrm{Met}(X)$ is equipped with the supremum distance. In this paper, for every strongly zero-dimensional metrizable space $X$, we prove that the set of all metrics whose ranges are closed totally disconnected subsets of the line is a dense $G_δ$ subspace in $\mathrm{Met}(X)$. As its application, we show that some sets of universal metrics are meager in spaces of metrics.
