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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Higher dimensional aposyndetic decompositions


Author: James T. Rogers Jr.
Journal: Proc. Amer. Math. Soc. 131 (2003), 3285-3288
MSC (2000): Primary 54F15; Secondary 54F50
Published electronically: February 14, 2003
MathSciNet review: 1992870
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Abstract | References | Similar Articles | Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06888-6
PII: S 0002-9939(03)06888-6
Keywords: Continuum, homogeneous, aposyndetic decomposition, terminal subcontinuum, cell-like
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
Article copyright: © Copyright 2003 American Mathematical Society