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    Covering Space

    Definition

    Suppose that X^~, X are arcwise-connected and locally arcwise-connected topological spaces. Then (X^~, p) is said to be a covering space of X if p:X^~->X is a surjective continuous map with every x element X having an open neighborhood U such that every connected component of p^(-1)(U) is mapped homeomorphically onto U by p.

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