In this paper, we study digital versions of some properties of covering spaces from algebraic topology. Among our results are some that correct or improve upon the presentation of assertions in earlier papers (Boxer and Karaca in J. Math. Imaging Vis. 32:23-29, 2008; Han in Inf. Sci. 177:3731-3748, 2007; Han in Inf. Sci. 178:550-561, 2008).