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Continuous Images of Arcs and Inverse Limit Methods
J. Nikiel, H. M. Tuncali, and E. D. Tymchatyn
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Memoirs of the American Mathematical Society
1993; 80 pp; softcover
Volume: 104
ISBN-10: 0-8218-2561-5
ISBN-13: 978-0-8218-2561-7
List Price: US$32
Individual Members: US$19.20
Institutional Members: US$25.60
Order Code: MEMO/104/498
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Continuous images of ordered continua have been studied intensively since 1960, when S. Mardšić 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.

Readership

Mathematicians interested in new developments in general topology, continuum theory, and dimension theory.

Table of Contents

  • Introduction
  • Cyclic elements in locally connected continua
  • T-sets in locally connected continua
  • T-maps, T-approximations 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
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