Suppose we have two covering spaces $p:\tilde X \rightarrow X$ and $q:\hat X \rightarrow X$ of the same space. Is the pullback $\tilde X \times_X \hat X$ also a covering space of $X$? If yes, what would be a proof?
2026-03-26 22:54:19.1774565659
Is the pullback of two covering spaces $\tilde X$ and $\hat X$ a covering space?
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being just a fiber bundle with discrete fibers - yes. Look at some proof of pullbacks of fiber bundles, which are used more often in general than in basic covering space theory. But good question!