论文标题
基本类固醇降低产品的产品
Transfinite product reduction in fundamental groupoids
论文作者
论文摘要
无限的产物，由无数的无限线性顺序索引，在基本类固醇的背景下自然出现。如果允许索引订单包含密集的子顺序，则将这些产品称为“转限”，否则称为“散射”。在本文中，我们证明了几种与基本类固醇中跨替代产物的减少（即因子组合）有关的技术引理。在应用这些结果时，我们表明，如果跨足基本的集体操作在空间$ x $中定义明确，并具有分散的代数$ 1 $ -WILD SET $ \ MATHBF {AW}（X）$，那么所有经过的thrfinite Gutteramental Groute grouperoid也均已很好地定义。
Infinite products, indexed by countably infinite linear orders, arise naturally in the context of fundamental groupoids. Such products are called "transfinite" if the index orders are permitted to contain a dense suborder and are called "scattered" otherwise. In this paper, we prove several technical lemmas related to the reduction (i.e. combining of factors) of transfinite products in fundamental groupoids. Applying these results, we show that if the transfinite fundamental group operations are well-defined in a space $X$ with a scattered algebraic $1$-wild set $\mathbf{aw}(X)$, then all transfinite fundamental groupoid operations are also well-defined.
