Memoirs of the American Mathematical Society 1993; 80 pp; softcover Volume: 104 ISBN10: 0821825615 ISBN13: 9780821825617 List Price: US$34 Individual Members: US$20.40 Institutional Members: US$27.20 Order Code: MEMO/104/498
 Continuous images of ordered continua have been studied intensively since 1960, when S. Mardšić showed that the classical HahnMazurkiewicz 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 wellplaced subsets which he called Tsets. 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 Tset 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. Readership Mathematicians interested in new developments in general topology, continuum theory, and dimension theory. Table of Contents  Introduction
 Cyclic elements in locally connected continua
 Tsets in locally connected continua
 Tmaps, Tapproximations and continuous images of arcs
 Inverse sequences of images of arcs
 \(1\)dimensional continuous images of arcs
 Totally regular continua
 Monotone images
 \(\sigma\)directed inverse limits
 References
