A Galois Correspondence with Generalized Covering Spaces

In this paper, we extend classical covering space theory to all connected and locally path connected spaces. This is accomplished using generalized covering spaces called semicovers and a (topological) group called the Galois fundamental group. It is shown for semilocally simply connected spaces that the theory is the same as the classical theory of covering spaces and the fundamental group. Lastly, we show that there is a topology on the fundamental group such that the completion is the Galois fundamental group