Covering Space

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 in X having an open neighborhood U such that every connected component of p^(-1)(U) is mapped homeomorphically onto U by p.

See also

Covering Map, Deck Transformation, Fundamental Group, Universal Cover

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Cite this as:

Weisstein, Eric W. "Covering Space." From MathWorld--A Wolfram Web Resource.

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