Mapping theorems for inverse limits with set-valued bonding functions (Q2091132)

In this paper, the authors obtain new mapping theorems for inverse limits of inverse sequences of compact metric spaces with continuous single-valued bonding functions. Then, by using Mioduszewski's and Feuerbacher's results from [\textit{G. A. Feuerbacher}, Houston J. Math. 20, No. 4, 713--719 (1994; Zbl 0839.54012); \textit{J. Mioduszewski}, Colloq. Math. 10, 39--44 (1963; Zbl 0118.18205)], they apply the results to the theory of inverse limits of inverse sequences of compact metric spaces with upper semicontinuous set-valued bonding functions to obtain new mapping theorems for such inverse limits. They give necessary and sufficient conditions for an inverse limit with upper semicontinuous set-valued bonding functions to have the fixed point property which answers an open problem stated by \textit{W. T. Ingram} [An introduction to inverse limits with set-valued functions. Berlin: Springer (2012; Zbl 1257.54033)].