Irreducibility in inverse limits of continua

This paper gives characterizations of irreducibility, indecomposability, and hereditary indecomposability for inverse limits of compact metric continua; the characterizations are in terms of the bonding maps. The characterization of indecomposability is used to get a characterization, in terms of covers, for indecomposability in any compact metric continuum. The latter result is applied to circle-like continua to got a characterization of indecomposability in terms of defining sequences of covers.