Continuous Images of Arcs and Inverse Limit Methods

Continuous images of ordered continua have been studied intensively since 1960, when S. Mard\v si\'c showed that the classical Hahn-Mazurkiewicz theorem does not generalize in the ''natural'' way to the nonmetric 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.Nikiel, J. is the author of 'Continuous Images of Arcs and Inverse Limit Methods' with ISBN 9780821825617 and ISBN 0821825615.