论文标题
重量的每个度量空间$λ=λ^{\ aleph_0} $允许在Banach空间
Every metric space of weight $λ=λ^{\aleph_0}$ admits a condensation onto a Banach space
论文作者
论文摘要
在本文中，我们已经证明，对于每个基数$λ$，因此$λ=λ^{\ aleph_0} $重量的度量空间$λ$允许在重量$λ$的Banach空间上进行射击的连续映射。然后，我们得到每个重量连续性的度量空间，都可以接收到Hilbert Cube上的一条族裔连续映射。这解决了著名的Banach的问题（何时是公制（可能是Banach）空间$ x $在重量连续体的度量标准中，将bi原始的连续映射到紧凑的公制空间上？）。同样，我们也知道，重量的每个度量空间$λ=λ^{\ aleph_0} $允许在Hausdorff紧凑型空间上进行射击的连续映射。这解决了Alexandroff问题（Hausdorff空间$ x $什么时候接纳了一群二级映射到Hausdorff紧凑型空间？
In this paper, we have proved that for each cardinal number $λ$ such that $λ=λ^{\aleph_0}$ a metric space of weight $λ$ admits a bijective continuous mapping onto a Banach space of weight $λ$. Then, we get that every metric space of weight continuum admits a bijective continuous mapping onto the Hilbert cube. This resolves the famous Banach's Problem (when does a metric (possibly Banach) space $X$ admit a bijective continuous mapping onto a compact metric space?) in the class of metric spaces of weight continuum. Also we get that every metric space of weight $λ=λ^{\aleph_0}$ admits a bijective continuous mapping onto a Hausdorff compact space. This resolves the Alexandroff Problem (when does a Hausdorff space $X$ admit a bijective continuous mapping onto a Hausdorff compact space?) in the class of metric spaces of weight $λ=λ^{\aleph_0}$.
