Let $X$ and $Y$ be topological spaces with a free G-action, where $G$ is group. Suppose $p:X\rightarrow Y$ is a Galois covering which is G-equivariant map. Then will it be true that the induced map $\tilde{p}:X/G\rightarrow Y/G$ is also a Galois covering?
Galois covering
2
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general-topology