Continuous Images of Arcs and Inverse Limit Methods (Memoirs of the American Mathematical Society)

Continuous Images of Arcs and Inverse Limit Methods (Memoirs of the American Mathematical Society)

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Description

Continuous images of ordered continua have been studied intensively since 1960, when S. Mardsic showed that the classical Hahn-Mazukiewicz theorem does not generalize in the 'natural' way to the non metric 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.

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.

Product Details

  • ISBN13: 9780821825617
  • Format: Paperback
  • Number Of Pages: 80
  • ID: 9780821825617
  • ISBN10: 0821825615

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