Abstract
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 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 the quotient space $Y$ is one.
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