标题： 连接标记群的空间和群运算的空间 显示英文标题

标题： Connecting the space of marked groups and the space of group operations

摘要： 我们建立两个广为研究的可数群空间之间的联系：群运算空间和标记群空间。 这种联系表明，这两个空间在Baire范畴意义上的泛性质方面是等价的，这使我们能够将一些结果从前者设置转换到后者。 作为应用，我们给出了两个关于紧致可度量阿贝尔群泛行为定理的新且更简短的证明。 显示英文摘要

摘要： We establish a connection between two well-studied spaces of countable groups: the space of group operations and the space of marked groups. This connection shows that the two spaces are equivalent in terms of generic properties in the sense of Baire category, which allows us to translate several results from the former setting to the latter. As an application, we give new, shorter proofs of two theorems that concern the generic behavior of compact metrizable abelian groups.