论文标题
细小形状iii：$δ$ - 空格和$ \ nabla $ - 空格
Fine shape III: $Δ$-spaces and $\nabla$-spaces
论文作者
论文摘要
在本文中，我们获得了结果，表明即使在非局部紧凑的情况下，精细的形状也是可行的，并且“不太强”，并且可以用来更好地理解无限尺寸的可衡量的可衡量空间及其同源理论。 我们表明，每个波兰空间$ x $都是良好的形状，等效于公制简单络合物之间的简单图的反向序列的极限。一个更深层次的结果是，如果$ x $是本地有限的维度，则可以选择简单的地图为非分类。如果$ x $是泰勒压缩，则不能选择它们为非分类。
In this paper we obtain results indicating that fine shape is tractable and "not too strong" even in the non-locally compact case, and can be used to better understand infinite-dimensional metrizable spaces and their homology theories. We show that every Polish space $X$ is fine shape equivalent to the limit of an inverse sequence of simplicial maps between metric simplicial complexes. A deeper result is that if $X$ is locally finite dimensional, then the simplicial maps can be chosen to be non-degenerate. They cannot be chosen to be non-degenerate if $X$ is the Taylor compactum.
