论文标题
可计数的密集均匀拓扑矢量空间是贝尔空间
A countable dense homogeneous topological vector space is a Baire space
论文作者
论文摘要
我们证明，每个包含Cantor套件的副本的同质均匀的均匀均匀拓扑空间都是Baire空间。特别是，每个可计数的密集均匀拓扑矢量空间都是贝尔空间。因此，对于任何非差异的Metrizable Space $ X $，功能空间$ C_P（X）$都不是可计数的密度均匀的。这回答了R.Hernández-Gutiérrez最近提出的一个问题。我们还得出结论，对于任何无限的Banach Space $ e $（双Banach Space $ e^\ ast $），配备了弱拓扑（$ e^\ ast $带有弱$^\ ast $ topology）的Space $ e $是不可计算的。我们概括了Hrušák，ZamoraAvilés和Hernández-Gutiérrez的一些结果，这些结果涉及可计数的密集均匀产品。
We prove that every homogeneous countable dense homogeneous topological space containing a copy of the Cantor set is a Baire space. In particular, every countable dense homogeneous topological vector space is a Baire space. It follows that, for any nondiscrete metrizable space $X$, the function space $C_p(X)$ is not countable dense homogeneous. This answers a question posed recently by R. Hernández-Gutiérrez. We also conclude that, for any infinite dimensional Banach space $E$ (dual Banach space $E^\ast$), the space $E$ equipped with the weak topology ($E^\ast$ with the weak$^\ast$ topology) is not countable dense homogeneous. We generalize some results of Hrušák, Zamora Avilés, and Hernández-Gutiérrez concerning countable dense homogeneous products.
