Pairs of indecomposable continua whose product is mutually aposyndetic
by
Alejandro Illanes
Universidad Nacional Autonoma de Mexico

A continuum is a compact connected metric space. A continuum X is said to be mutually aposyndetic provided that for any two distinct points x and y in X, there exist two subcontinua L and M of X such that x in int_X(L) and y in int_X(M). A continuum X is said to be strictly non-mutual aposyndetic if each pair of subcontinua of X which have interiors intersect. The concept of mutual aposyndesis was introduced by Charles L. Hagopian. He proved that, the product of two chainable continua is strictly non-mutually aposyndetic if and only if each factor is indecomposable. He also asked the question: Is the topological product of two indecomposable compact metric continua strictly non-mutually aposyndetic?

In this paper we answer Hagopian's question in the negative by showing that the product S_p ×S_q is mutually aposyndetic, where for an integer m > 1, S_m is the m-adic solenoid and p and q are relative primes.

Date received: February 17, 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-07.