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.
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.