Mathematics – Metric Geometry
Scientific paper
2007-06-26
Mathematics
Metric Geometry
26 pages. The paper was split and the second part is available at arXiv:0802.4304
Scientific paper
James \cite{Jam} introduced uniform covering maps as an analog of covering maps in the topological category. Subsequently Berestovskii and Plaut \cite{BP3} introduced a theory of covers for uniform spaces generalizing their results for topological groups \cite{BP1}-\cite{BP2}. Their main concepts are discrete actions and pro-discrete actions, respectively. In case of pro-discrete actions Berestovskii and Plaut provided an analog of the universal covering space and their theory works well for the so-called coverable spaces. As will be seen in Section \ref{SECTION-Comparison}, \cite{BP3} generalizes only regular covering maps in topology and pro-discrete actions may not be preserved by compositions. In this paper we redefine the uniform covering maps and we generalize pro-discrete actions using Rips complexes and the chain lifting property. We expand the concept of generalized paths of Krasinkiewicz and Minc \cite{KraMin}.
Brodskiy N.
Dydak Jerzy
Labuz Brendon
Mitra Aditi
No associations
LandOfFree
Rips complexes and covers in the uniform category 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 Rips complexes and covers in the uniform category, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rips complexes and covers in the uniform category will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-255329