论文标题
关于局部紧凑的可分开度量空间的强同源性的可添加性
On the additivity of strong homology for locally compact separable metric spaces
论文作者
论文摘要
我们表明，相对于弱紧凑的基本主教是一致的，强大的同源性是加性的，并且在局部可分开的度量空间的类别中得到了紧凑的支持。这补充了Mardešić和Prasolov的工作，表明连续假设意味着可数的夏威夷耳环总和见证了强有力的同源性未能具有这些特性中的任何一种。我们的结果直接建立在Lambie-Hanson和第二作者的基础上，该作者建立了相对于$ \ Mathrm {lim}^S \ Mathbf {a} = 0 $的一致性，相对于弱紧凑的红衣主教，用于所有$ s \ geq 1 $ for All $ s \ geq 1 $ for All $ s \ geq 1 $ for All $ s \ geq 1 $我们表明，该作品的论点对$ \ mathrm {lim}^s $ fuctors的消失和添加性具有影响，这是由$ \ mathbb {n}^{\ mathbb {n}} $索引的基本更一般类的Pro-Abelian群体的影响。
We show that it is consistent relative to a weakly compact cardinal that strong homology is additive and compactly supported within the class of locally compact separable metric spaces. This complements work of Mardešić and Prasolov showing that the Continuum Hypothesis implies that a countable sum of Hawaiian earrings witnesses the failure of strong homology to possess either of these properties. Our results build directly on work of Lambie-Hanson and the second author which establishes the consistency, relative to a weakly compact cardinal, of $\mathrm{lim}^s \mathbf{A} = 0$ for all $s \geq 1$ for a certain pro-abelian group $\mathbf{A}$; we show that that work's arguments carry implications for the vanishing and additivity of the $\mathrm{lim}^s$ functors over a substantially more general class of pro-abelian groups indexed by $\mathbb{N}^{\mathbb{N}}$.
