Methods of constructing spaces with non-trivial self covers

TL;DR

This paper surveys techniques for constructing topological spaces with non-trivial self covers, discussing methods, related group theoretic and topological issues, and open problems.

Contribution

It provides a comprehensive overview of methods for building spaces with non-trivial self covers and discusses related mathematical concerns and open questions.

Findings

Methods for constructing low and high dimension continua with self covers

Discussion of group theoretic and topological issues related to self covers

Presentation of open problems in the field

Abstract

We survey techniques for constructing spaces with non-trivial self covers. These processes include methods for building low and high dimension continua which non-trivially self. We also discuss several related group theoretic and topological concerns. Statements of a number of open problems related to self covering phenomena are included.