Higher-dimensional aposyndetic decompositions
by
James T. Rogers, Jr.
Tulane University

Let X be a homogeneous, decomposable continuum that is not aposyndetic. The Aposyndetic Decomposition Theorem yields a cell-like decomposition of X into homogeneous continua with quotient space Y being an aposyndetic, homogeneous continuum.

Assume that the dimension of X is greater than one. About 20 years ago the author asked the following questions: Can this aposyndetic decomposition raise dimension? Can it lower dimension? We answer these questions by proving the following theorem:

Theorem The dimension of Y is one.

Consequences and other theorems along this line will be discussed.

Date received: February 8, 2001