论文标题
某些功能空间的Baire属性
Baire property of some function spaces
论文作者
论文摘要
紧凑型空间$ x $称为$π$ - 单石器时代，如果对于任何过滤的连续映射$ f：x \ rightarrow k $，其中$ k $是一个可METRIZABLIXABLIXABLIZABL SPACE，则存在一个可METRIXABLIZABLIZABLIZABLIZABLIZABLIZACT SPACE $ T \ subseteq X $，例如$ f（t）= k $。如果任何$ 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 $是baire。令$ c_p（x，y）$表示所有连续$ y $ - 值$ c（x，y）$ tychonoff space $ x $的空间，并带有尖端融合的拓扑。在本文中，我们已经证明，对于完全断开的空间$ x $，空间$ c_p（x，\ {0,1 \}）$是baire的，并且只有$ c_p（x，k）$是每一个$π$ monolithic-monolithic compact Space $ k $ k $。对于tychonoff space $ x $ x $ space $ c_p（x）$是baire，并且只有$ c_p（x，l）$是每个Frechet Space $ L $的baire。我们构建了一个完全断开的Tychonoff Space $ t $，这样$ C_P（T，M）$是可分开的度量空间$ M $的Baire，并且只有当$ m $是Peano Continum。此外，$ c_p（t，[0,1]）$是baire，但是$ cp（t，\ {0,1 \}）$不是。
A compact space $X$ is called $π$-monolithic if for any surjective continuous mapping $f:X\rightarrow K$ where $K$ is a metrizable compact space there exists a metrizable compact space $T\subseteq X$ such that $f(T)=K$. A topological space $X$ is Baire if the intersection of any sequence of open dense subsets of $X$ is dense in $X$. Let $C_p(X,Y)$ denote the space of all continuous $Y$- valued functions $C(X,Y)$ on a Tychonoff space $X$ with the topology of pointwise convergence. In this paper we have proved that for a totally disconnected space $X$ the space $C_p(X,\{0,1\})$ is Baire if, and only if, $C_p(X,K)$ is Baire for every $π$-monolithic compact space $K$. For a Tychonoff space $X$ the space $C_p(X)$ is Baire if, and only if, $C_p(X,L)$ is Baire for each Frechet space $L$. We construct a totally disconnected Tychonoff space $T$ such that $C_p(T,M)$ is Baire for a separable metric space $M$ if, and only if, $M$ is a Peano continuum. Moreover, $C_p(T,[0,1])$ is Baire but $Cp(T,\{0,1\})$ is not.
