In this paper we work in an arbitrary o-minimal structure with definable Skolem functions and prove that definably connected, locally definable manifolds are uniformly definably path connected, have an admissible cover by definably simply connected, open definable subsets and, definable paths and definable homotopies on such locally definable manifolds can be lifted to locally definable covering maps. These properties allow us to obtain the main properties of the general o-minimal fundamental group, including: invariance and comparison results; existence of universal locally definable covering maps; monodromy equivalence for locally constant o-minimal sheaves – from which one obtains, as in algebraic topology, classification results for locally definable covering maps, o-minimal Hurewicz and Seifert–van Kampen theorems.

在本文中，我们在具有可定义的Skolem函数的任意o最小结构中工作，并证明了确定连接的，局部可定义的流形一致地确定的路径连接，并通过确定简单地连接，开放的可定义子集以及可定义的路径和可定义的同伦性而具有可容许的覆盖在此类本地可定义的歧管上，可以将其提升到本地可定义的覆盖图。这些特性使我们能够获得一般o最小基本基团的主要特性，包括：不变性和比较结果；存在通用的本地可定义覆盖图；局部恒定的O最小滑轮的单峰等效性-从其中获得一个代数拓扑，对局部可定义的覆盖图，O最小Hurewicz和Seifert-van Kampen定理进行分类。