Generalized Universal Covers of Uniform Spaces

Details Generalized Universal Covers of Uniform Spaces Generalized Universal Covers of Uniform Spaces

2006-07-14

arxiv.org/abs/math/0607353v1

Mathematics

Algebraic Topology

Scientific paper

We develop a generalized covering space theory for a class of uniform spaces called coverable spaces. Coverable spaces include all geodesic metric spaces, connected and locally pathwise connected compact topological spaces, in particular Peano continua, as well as more pathological spaces like the topologist's sine curve. Each coverable space has a generalized universal cover with universal and lifting properties. Associated with this generalized universal cover is a functorial uniform space invariant called the deck group, which is related to the classical fundamental group by a natural homomorphism. We obtain some specific results for one-dimensional spaces. Keywords: universal cover, uniform space, geodesic space, fundamental group

Affiliated with

Also associated with

No associations

Rating

Generalized Universal Covers of Uniform Spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Generalized Universal Covers of Uniform Spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized Universal Covers of Uniform Spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-97273