Continua: With the Houston Problem Book / Edition 1

by Howard Cook

Overview

This volume contains the proceedings of the special session on Modern Methods in Continuum Theory presented at the 100th Annual Joint Mathematics Meetings held in Cincinnati, Ohio. It also features the Houston Problem Book which includes a recently updated set of 200 problems accumulated over several years at the University of Houston.;These proceedings and problems are aimed at pure and applied mathematicians, topologists, geometers, physicists and graduate-level students in these disciplines.

Product Details

ISBN-13:	9780824796501
Publisher:	Taylor & Francis
Publication date:	03/23/1995
Series:	Lecture Notes in Pure and Applied Mathematics , #170
Pages:	416
Product dimensions:	8.25(w) x 11.00(h) x (d)

About the Author

HOWARD COOK is a Professor of Mathematics at the University of Houston, Texas. A member of the American Mathematical Society, Professor Cook received the Ph.D. degree (1962) from the University of Texas, Austin. W. T. Ingram is a Professor of Mathematics and Chairman of the Department of Mathematics and Statistics at the University of Missouri—Rolla. A member of the American Mathematical Society and the Mathematical Association of America, Professor Ingram received the Ph.D. degree (1964) from Auburn University, Alabama. K. T. Kuperberg is a Professor of Mathematics at Auburn University, Alabama. A member of the American Mathematical Society, among others, Professor Kuperberg received the Ph.D. degree (1974) from Rice University, Houston, Texas. Andrew Lelek is a Professor of Mathematics at the University of Houston, Texas. A member of the American Mathematical Society, Professor Lelek received the Ph.D. degree (1959) from the University of Wroclaw, Poland. . Piotr Minc is a Professor of Mathematics at Auburn University, Alabama. A member of the American Mathematical Society, Professor Minc received the Ph.D. degree (1974) from Warsaw University, Poland.

Table of Contents

Part 1 Expository and survey papers: matchbox manifolds; rotation sets for invariant continua; the fixed point property in dimension one; Menger manifolds; exactly k-to-1 functions - from pathological functions with finitely many discontinuities to well-behaved covering maps; a brief history of indecomposable continua; spans of continua and their applications; complex dynamics and continuum theory; continua on which 2-to-1 maps induce continuous involutions. Part 2 Research papers: end-points of inverse limit spaces and dynamics; essential span of simple closed curves; invertibility of the pseudoarc; inverse limit spaces, periodic points and arcs; a three dimensional prime end theory; a symbolic representation of inverse limit spaces for a class of unimodal maps; semi-aposyndesis and continuum chainability; inverse limits on [0,1] using tent maps and certain other piecewise linear bonding maps; on composants of indecomposable subcontinua of surfaces; minimal sets and chaos in the sense of devaney on continuum-wise expansive homeomorphisms; characterizations of Menger manifolds and Hilbert cube manifolds in terms of partitions; homology separation and 2-homogeneity; solenoids and bihomogeneity; openly homogeneous continua in 2-manifolds - a generalization of a theorem of Bing; a continuous decomposition of the Sierpinsky curve; extensions of Jakobsche's construction of n-homogeneous continua. Part 3 The Houston problem book: a list of problems known as Houston problem book.

Editorial Reviews

The proceedings of the Modern Methods in Continuum Theory session at the Annual Joint Mathematics Meetings in Cincinnati, Ohio, January 1994, augmented by the Houston Problem Book, a collection of over 200 problems accumulated over several years at the University of Houston, and frequently used by continuum theorists but never published before. Nine of the 26 papers are surveys and expositions; among their topics are matchbox and Menger manifolds, spans of continua and their applications, and the fixed point property in dimension one. The others report on such research as the essential span of simple closed curves, composants of indecomposable subcontinua of surfaces, and solenoids and bihomogeneity. Reproduced from typescripts. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews