We study a natural generalization of inverse systems of finite regular covering spaces. A limit of such a system is a fibration whose fibres are profinite topological groups. However, as shown in a previous paper (Conner-Herfort-Pavesic: Some anomalous examples of lifting spaces), there are many fibrations whose fibres are profinite groups, which are far from being inverse limits of coverings. We characterize profinite fibrations among a large class of fibrations and relate the profinite topology on the fundamental group of the base with the action of the fundamental group on the fibre, and develop a version of the Borel construction for fibrations whose fibres are profinite groups.

中文翻译：

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紧凑提升空间的几何形状

我们研究了有限规则覆盖空间的逆系统的自然推广。这种系统的一个极限是其纤维是有限拓扑群的纤维化。然而，如前一篇论文（Conner-Herfort-Pavesic：提升空间的一些异常例子）所示，有许多纤维是超限群的纤维化，远非覆盖的逆极限。我们表征了一大类纤维中的超细纤维，并将基础基群上的超细拓扑与基本群对纤维的作用联系起来，并开发了一种用于纤维是超细群的纤维的 Borel 构造版本。