Unicoherence by Approximation
by
Robert Allen Pierce
University of Wisconsin, Superior

In this paper G denotes a type of irreducible covering of a continuum X by subcontinua, and each continuum that is a union of elements of G is called a G-continuum. Generalizing the usual definition of unicoherence, we define G-unicoherence for G-continua. It is shown that X is G-unicoherent for arbitrarily fine coverings, G, if and only if X is unicoherent in the usual sense. Conditions are given under which a G-continuum that is the closure of a union of G-unicoherent G-continua is itself G-unicoherent. (One of the conditions is that G be a closed subspace of the hyperspace C(X).) These results are used to demonstrate the unicoherence of a compactified three-dimensional spiral whose remainder is the first non-simply connected approximant of Menger's Universal Curve. This example is itself intended as a first approximation to a continuum that is unicoherent, one-dimensional and n-mutually aposyndetic for each integer n > 1, but not locally connected.

Date received: June 30, 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 # caao-56.