Continuous Images of Arcs and Inverse Limit Methods
( Memoirs of the American Mathematical Society )
Publication series ：Memoirs of the American Mathematical Society
Author： J. Nikiel
Publisher： American Mathematical Society
Publication year： 2013
E-ISBN: 9781470400750
P-ISBN(Paperback): 9780821825617
Subject： O189.11 topological space (topological space)
Keyword： Geometry and Topology
Language： ENG
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Continuous Images of Arcs and Inverse Limit Methods
Description
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.