universal covering space
If is based, with basepoint , then a based cover of is cover of which is also a based space with a basepoint such that the covering is a map of based spaces. Note that any cover can be made into a based cover by choosing a basepoint from the pre-images of .
Clearly, if a universal covering exists, it is unique up to unique isomorphism. But not every topological space has a universal cover. In fact has a universal cover if and only if it is semi-locally simply connected (for example, if it is a locally finite CW-complex or a manifold).
|Title||universal covering space|
|Date of creation||2013-03-22 12:15:34|
|Last modified on||2013-03-22 12:15:34|
|Last modified by||bwebste (988)|