**Memoirs of the American Mathematical Society**

1993;
80 pp;
Softcover

MSC: Primary 54;

Print ISBN: 978-0-8218-2561-7

Product Code: MEMO/104/498

List Price: $34.00

Individual Member Price: $20.40

**Electronic ISBN: 978-1-4704-0075-0
Product Code: MEMO/104/498.E**

List Price: $34.00

Individual Member Price: $20.40

# Continuous Images of Arcs and Inverse Limit Methods

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*J. Nikiel; H. M. Tuncali; E. D. Tymchatyn*

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

# Table of Contents

## Continuous Images of Arcs and Inverse Limit Methods

- List of Contents v6 free
- 1. Introduction 110 free
- 2. Cyclic elements in locally connected continua 514 free
- 3. T-sets in locally connected continua 1423
- 4. T-maps, T-approximations and continuous images of arcs 2029
- 5. Inverse sequences of images of arcs 2433
- 6. 1-dimensional continuous images of arcs 3140
- 7. Totally regular continua 4554
- 8. Monotone images 6170
- 9. σ-directed inverse limits 7382
- References 7786