Inverse limits of simplicial maps of graphs
by
Piotr Minc
Auburn University

A continuum X is homeomorphic to the inverse limit of graphs with simplicial bonding maps if it contains a compact set Z such that dim(Z) <= 0 and each point in X\Z has a neighborhood homeomorphic to the product of a zero-dimensional set and the real line. Moreover, if all arc-components of X\Z have their diameters greater than some positive \epsilon, one can require the bonding maps to be light. (A simplicial map between graphs is light if it maps every edge onto an edge.) The above characterization shows that many, if not most, of the classical examples in the continuum theory are inverse limits of graphs with simplicial (and light) bonding maps. It is natural, therefore, to revisit some old open questions and rephrase them for continua that are homeomorphic to limits of graphs with simplicial (and perhaps light) bonding maps.

Date received: February 27, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caam-26.