Inverse limits of uniform covering maps (Q411825)

The author investigates the concept of uniform covering maps as defined by [\textit{N. Brodskiy}, \textit{J. Dydak}, \textit{B. Labuz} and \textit{A. Mitra}, ``Rips complexes and covers in the uniform category'', \url{arXiv:0706.3937}] and its connection to inverse limits. The following questions are answered: {\parindent=6mm \begin{itemize}\item[{\(\bullet\)}] Under what condition does a generalized uniform covering map correspond to the inverse limit of appropriate uniform covering maps over the same space? \item[{\(\bullet\)}] Under what condition does the inverse limit of uniform covering maps over the same space induce a generalized uniform covering map? \item[{\(\bullet\)}] What is a characterization of the generalized uniform covering maps that arise from group actions in terms of inverse limits? \item[{\(\bullet\)}] Suppose \(X\) is an appropriate inverse limit of compact spaces \(X_i\). Under what conditions is a generalized uniform covering space of \(X\) an inverse limit of covering spaces over \(X_i\)?NEWLINENEWLINE\end{itemize}}