# 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…

## 14 Citations

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On Topologized Fundamental Group and covering spaces of topological groups

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In this paper, we show that every topological group is a strong small loop transfer space at the identity element. This implies that the quasitopological fundamental group of a connected locally path…

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On Topologized Fundamental Groups with Small Loop Transfer Viewpoints

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In this paper, by introducing some kind of small loop transfer spaces at a point, we study the behavior of topologized fundamental groups with the compact-open topology and the whisker topology,…

On strong small loop transfer spaces relative to subgroups of fundamental groups

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On Subgroups of Topologized Fundamental Groups and Generalized Coverings

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In this paper, we are interested in study subgroups of topologized fundamental groups and their influences on generalized covering maps. More precisely, we find some relationships between generalized…

On Topological Homotopy Groups and Relation to Hawaiian Groups

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By generalizing the whisker topology on the $n$th homotopy group of pointed space $(X, x_0)$, denoted by $\pi_n^{wh}(X, x_0)$, we show that $\pi_n^{wh}(X, x_0)$ is a topological group if $n \ge 2$.…

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