Jacek Nikiel's Books

Continuous Images of Arcs and Inverse Limit Methods

By: Jacek Nikiel,H. M. Tuncali,E. D. Tymchatyn

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Continuous Images of Arcs and Inverse Limit Methods

By: Jacek Nikiel,H. M. Tuncali,E. D. Tymchatyn

Continuous images of ordered continua are investigated. The paper gives various properties of their monotone images and inverse limits of their inverse systems (or sequences) with monotone bonding surjections. Some factorization theorems are provided. Special attention is given to one-dimensional spaces which are continuous images of arcs and, among them, various classes of rim-finite continua. The methods of proofs include cyclic element theory, T-set approximations and null-family decompositions. The paper brings also new properties of cyclic elements and T-sets in locally connected continua, in general.

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American Mathematical Soc.

Published Date

ISBN 10

0821825615

ISBN 13

9780821825617

Topologies on Pseudo-Trees and Applications

By: Jacek Nikiel

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Topologies on Pseudo-Trees and Applications

By: Jacek Nikiel

A pseudo-tree is a partially ordered set such that the set of all predecessors of any element is linearly ordered. Clearly, each linearly ordered set is a pseudo-tree and pseudo-trees are, in general, much more complicated objects than chains. The aim of this paper is to develop a theory of natural order topologies on pseudo-trees which extends the theories of linearly ordered topological spaces and GO-spaces. Moreover, applications are given for some classes of continua which admit a natural ordering.

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126

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821824791

ISBN 13

9780821824795

Continuous Images of Arcs and Inverse Limit Methods

By: Jacek Nikiel

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Continuous Images of Arcs and Inverse Limit Methods

By: Jacek Nikiel

Continuous images of ordered continua have been studied intensively since 1960, when S. Mardvsic 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.

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