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    discrete topology

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    A covering map is a map p: E -> B with the property that each point b, an element of B, has a neighborhood U such that p^-1(U) is a disjoint union of open sets V_alpha such that, for each alpha, the restriction of p to V_alpha is a homeomorphism of V_alpha onto U.

    Show that, if Y has the discrete topology and if p: X x Y --> X is the projection onto the first factor, then p is a covering map.

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    Solution Preview

    In the discrete topology all subsets are open. In particular, all sets that contain a single point are open.

    Let x be in X, and B is an ...

    Solution Summary

    This solution contextualizes discrete topology.