# How to find n-sheeted covering space of a topological space explicitly(If exists)?

We know that there is a one to one Galois correspondence between subgroups of the fundamental group of some topological space and covering space for a path connected and locally path connected topological space.suppose n-sheeted covering space exist for some topological space X.So if I want to construct n-sheeted covering space explicitly then what is the general way to find that?

• Note that the $n$-covering might correspond to different subgroups. – Daniel Valenzuela Feb 24 '15 at 0:01
• yes..that's right... – Ripan Saha Feb 24 '15 at 2:01
• Write down the universal cover. Pick the index $n$ subgroup corresponding to a specific $n$-sheeted covering space, and quotient the universal cover out by the action of this subgroup. You get the desired covering space. – user98602 Feb 26 '15 at 17:23