Electronic ISBN:  9781470400750 
Product Code:  MEMO/104/498.E 
List Price:  $34.00 
MAA Member Price:  $30.60 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 104; 1993; 80 ppMSC: Primary 54;
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.
ReadershipMathematicians interested in new developments in general topology, continuum theory, and dimension theory.

Table of Contents

Chapters

1. Introduction

2. Cyclic elements in locally connected continua

3. Tsets in locally connected continua

4. Tmaps, Tapproximations and continuous images of arcs

5. Inverse sequences of images of arcs

6. 1dimensional continuous images of arcs

7. Totally regular continua

8. Monotone images

9. $\sigma $directed inverse limits


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

Chapters

1. Introduction

2. Cyclic elements in locally connected continua

3. Tsets in locally connected continua

4. Tmaps, Tapproximations and continuous images of arcs

5. Inverse sequences of images of arcs

6. 1dimensional continuous images of arcs

7. Totally regular continua

8. Monotone images

9. $\sigma $directed inverse limits