Higher dimensional aposyndetic decompositions

Rogers, James, Jr.

doi:10.1090/S0002-9939-03-06888-6

Higher dimensional aposyndetic decompositions
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by James T. Rogers Jr. PDF

Proc. Amer. Math. Soc. 131 (2003), 3285-3288 Request permission

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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