Inverse limits with irreducible set-valued functions (Q2440856)

In 1982 \textit{W. T. Watkins} [Pac. J. Math. 103, 589--601 (1982; Zbl 0451.54027)] classified Knaster type continua in terms of inverse limits of open piecewise monotone functions. Let \(K_p\) be the Knaster type continuum obtained as the inverse limit of \(p\)th degree tent maps. Watkins showed that \(K_n\) and \(K_m\) are homeomorphic if and only if \(m\) and \(n\) have the same prime factors. Recently, Scott Varagona showed that a particular N-shaped set valued function gives the generalized inverse limit homeomorphic to \(K_3\), opening doors for further generalizations. Inspired by Varagona's results and methods, the author of the article under review extends the results of Watkins to a wider class of generalized inverse limits. The criteria he provides can be used in many cases to distinguish non-homeomorphic generalized inverse limits by examination of combinatorial properties of graphs of set-valued functions, or detect indecomposability. The proofs rely on the notion of set-valued functions given by irreducible collections of maps and itinerary maps of such collections.