论文标题
在Baire属性，紧凑性和Baire功能空间的完整性
On Baire property, compactness and completeness properties of spaces of Baire functions
论文作者
论文摘要
如果任何$ x $的开放式密度子集的交叉点在$ x $中是密集的，则拓扑空间$ x $是baire。 Baire功能空间的有趣问题之一是Banakh-Gabriylyan问题：让$α$成为可数的序数。表征拓扑空间$ x $和$ y $，功能空间$b_α（x，y）$是baire。在本文中，对于任何Frechet Space $ y $，我们都获得了一个表征拓扑空间$ x $，该功能空间$b_α（x，y）$是baire。特别是，我们证明$b_α（x，\ mathbb {r}）$是baire时，并且仅当$b_α（x，y）$都是baire的任何banach space $ y $。另外，我们证明了许多Frechet Space $ y $的空间中的许多完整性和紧凑属性重合$B_α（x，y）$。
A topological space $X$ is Baire if the intersection of any sequence of open dense subsets of $X$ is dense in $X$. One of the interesting problems for the space of Baire functions is the Banakh-Gabriyelyan problem: Let $α$ be a countable ordinal. Characterize topological spaces $X$ and $Y$ for which the function space $B_α(X,Y)$ is Baire. In this paper, for any Frechet space $Y$ , we have obtained a characterization topological spaces $X$ for which the function space $B_α(X,Y)$ is Baire. In particular, we proved that $B_α(X,\mathbb{R})$ is Baire if and only if $B_α(X,Y)$ is Baire for any Banach space $Y$. Also we proved that many completeness and compactness properties coincide in spaces $B_α(X,Y)$ for any Frechet space $Y$.
