Suppose that are arcwise-connected and locally arcwise-connected topological spaces. Then is said to be a covering space of if is a surjective continuous map with every having an open neighborhood such that every connected component of is mapped homeomorphically onto by .

# Covering Space

## See also

Covering Map, Deck Transformation, Fundamental Group, Universal Cover## Explore with Wolfram|Alpha

## Cite this as:

Weisstein, Eric W. "Covering Space." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/CoveringSpace.html