• Corpus ID: 118558800

TOPOLOGICAL AND UNIFORM STRUCTURES ON UNIVERSAL COVERING SPACES

@article{Brodskiy2012TOPOLOGICALAU,
  title={TOPOLOGICAL AND UNIFORM STRUCTURES ON UNIVERSAL COVERING SPACES},
  author={N. Brodskiy and Jerzy Dydak and B. Labuz and A. Mitra},
  journal={arXiv: Algebraic Topology},
  year={2012}
}
We discuss various uniform structures and topologies on the uni- versal covering space e X and on the fundamental group �1(X, x0). We intro- duce a canonical uniform structure CU(X) on a topological space X and use it to relate topologies on e X and uniform structures on ^ CU(X). Using our concept of universal Peano space we show connections between the topology introduced by Spanier (30) and a uniform structure of Berestovskii and Plaut (2). We give a sufficient and necessary condition… 
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References

SHOWING 1-10 OF 26 REFERENCES
Uniform universal covers of uniform spaces
Uniform Spaces, I
Covering maps for locally path-connected spaces
We define Peano covering maps and prove basic properties analogous to classical covers. Their domain is always locally path-connected but the range may be an arbitrary topological space. One of
Topological Groups and Related Structures
[i]Topological Groups and Related Structures[/i] provides an extensive overview of techniques and results in the topological theory of topological groups. This overview goes sufficiently deep and is
The fundamental group of a compact metric space
We give a forcing free proof of a conjecture of Mycielski that the fundamental group of a connected locally connected compact metric space is either finitely generated or has the power of the
Small loop spaces
Quotients of uniform spaces
Introduction To Uniform Spaces
Introduction 1. Uniform structures 2. Induced and coinduced uniform structures 3. The uniform topology 4. Completeness and completion 5. Topological groups 6. Uniform transformation groups 7. Uniform
...
1
2
3
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