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:	9781138430280
Publisher:	Taylor & Francis
Publication date:	07/27/2017
Series:	Lecture Notes in Pure and Applied Mathematics
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

Preface — Part I. Expository and Survey Papers — 1. Matchbox manifolds /byJan M. Aarts and Lex G. Oversteegen — 2. Rotation sets for invariant continua /by Kathleen T. Alligood — 3. The fixed point property in dimension one /by David P. Bellamy — 4. Menger manifolds /byAlex Chigogidze, Kazuhiro Kawamura and E. D. Tymchatyn — 5. Exactly fc-to-1 functions: from pathological functions with finitely many discontinuities to well-behaved covering maps /by Jo W. Heath — 6. A brief history of indecomposable continua /by Judy A. Kennedy — 7. Spans of continua and their applications /by Andrew Lelek and Thelma West — 8. Complex dynamics and continuum theory /by John C. Mayer — 9. Continua on which 2-to-l maps induce continuous involutions /by Jerzy Mioduszewski — Part II. Research Papers — 10. Endpoints of inverse limit spaces and dynamics /by Marcy Barge and Joe Martin — 11. The essential span of simple closed curves /by Marcy Barge and Richard Swanson — 12. Invertibility of the pseudo-arc /by David P. Bellamy — 13. Inverse limit spaces, periodic points, and arcs /by Louis Block and Shannon Schumann — 14. A symbolic representation of inverse limit spaces for a class of unimodal maps /by Karen M. Bracks and Beverly Diamond — 15. On the homotopic structure of dynamical systems containing global attractors /by Bemd Gunther — 16. Semi-aposyndesis and continuum chainability /by Charles L. Hagopian and Lex G. Oversteegen — 17. Inverse limits on [0,1] using tent maps and certain other piecewise linear bonding maps /by W. T. Ingram — 18. On composants of indecomposable subcontinua of surfaces /by Zbigniew Kamo — 19. Minimal sets and chaos in the sense of Devaney on continuum-wise expansive homeomorphisms /by Hisao Kato — 20. Characterizations of Menger manifolds and Hilbert cube manifolds in terms of partitions /by Kazuhiro Kawamura — 21. Homology separation and 2-homogeneity /by KrystynaKuperberg, Wlodzimierz Kuperberg and William R. R. Transue — 22. Solenoids and bihomogeneity /by Piotr Minc — 23. Openly homogeneous continua in 2-manifolds: A generalization of a theorem of Bing /by Janusz R. Prajs — 24. A continuous decomposition of the Sierpinski curve /by Carl R. Seaquist — 25. A wild fc-dimensional Menger compactum in R2k+1, all cell-like subsets of which are cellular /by Richard B. Sher — 26. An extension of Jakobsche’s construction of n-homogeneous continua to the nonorientable case /by Paul R. Stallings — Part III. The Houston Problem Book — 27. A list of problems known as Houston Problem Book /by Howard Cook, W. T. Ingram and Andrew Lelek — Index.

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