Higher dimensional aposyndetic decompositions
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- by James T. Rogers Jr. PDF
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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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Additional Information
- James T. Rogers Jr.
- Affiliation: Department of Mathematics, Tulane University, New Orleans, Louisiana 70118
- Email: jim@math.tulane.edu
- Received by editor(s): July 19, 2001
- Received by editor(s) in revised form: May 9, 2002
- Published electronically: February 14, 2003
- Communicated by: Ronald A. Fintushel
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 3285-3288
- MSC (2000): Primary 54F15; Secondary 54F50
- DOI: https://doi.org/10.1090/S0002-9939-03-06888-6
- MathSciNet review: 1992870