Graph-like spaces: An introduction

Thomassen and Vella (Graph-like continua, augmenting arcs, and Menger’s Theorem, Combinatorica, http://dx.doi.org/10.1007/s00493-008-2342-9) have recently introduced the notion of a graph-like space, simultaneously generalizing infinite graphs and many of the compact spaces recently used by Diestel or Richter (and their coauthors) to study cycle spaces and related problems in infinite graphs. This work is a survey to introduce graph-like spaces and shows how many of these works on compact spaces can be generalized to compact graph-like spaces.