Continuous Images of Arcs and Inverse Limit Methods

Studies images of arcs using T-set approximations and inverse limits with monotone bonding maps. This book presents a number of theorems on Peano continua that are extended to the images of arcs.

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Continuous images of ordered continua have been studied intensively since 1960, when S. Mardsic showed that the classical Hahn-Mazukiewicz theorem does not generalize in the 'natural' way to the non metric case. In 1986, Nikiel characterized acyclic images of arcs as continua which can be approximated from within by a sequence of well-placed subsets which he called T-sets. That characterization has been used to answer a host of outstanding questions in the area. In this book, Nikiel, Tymchatyn, and Tuncali study images of arcs using T-set approximations and inverse limits with monotone bonding maps. A number of important theorems on Peano continua are extended to images of arcs. Some of the results presented here are new even in the metric case.