|
Higher dimensional aposyndetic decompositions
Author(s):
James
T.
Rogers Jr.
Journal:
Proc. Amer. Math. Soc.
131
(2003),
3285-3288.
MSC (2000):
Primary 54F15;
Secondary 54F50
Posted:
February 14, 2003
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
Let  be a homogeneous, decomposable continuum that is not aposyndetic. The Aposyndetic Decomposition Theorem yields a cell-like decomposition of  into homogeneous continua with quotient space  being an aposyndetic, homogeneous continuum. Assume the dimension of  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  is one.
References:
-
- [B]
- R. H. Bing, Higher dimensional hereditarily indecomposable continua., Trans. Amer. Math. Soc. 21 (1951), 267-273. MR 13:265c
- [HW]
- W. Hurewicz and J. Wallman, Dimension Theory, Princeton Univ. Press, Princeton, N.J., 1948.
- [J1]
- F. Burton Jones, The aposyndetic decomposition of homogeneous continua, Topology Proc. 8 (1983), 51-54. MR 85g:54023
- [J2]
- F. Burton Jones, Certain homogeneous unicoherent indecomposable continua, Proc. Amer. Math. Soc. 2 (1951), 855-859. MR 13:573a
- [Kra]
- J. Krasinkiewicz, On mappings with hereditarily indecomposable fibers, Bull. Polish Acad. Sci. Math. 44 (1996), 147-156. MR 97g:54016
- [Kru]
- P. Krupski, The disjoint arcs property for homogeneous curves, Fund. Math. 146 (1995), 159-169. MR 96a:54049
- [L]
- M. Levin, Bing maps and finite dimensional maps, Fund. Math. 151 (1996), 47-52. MR 97e:54031
- [N]
- S. B. Nadler, Jr., Continuum Theory, Marcel Dekker, Inc. New York, 1992. MR 93m:54002
- [R1]
- J. T. Rogers, Jr., Cell-like decompositions of homogeneous continua, Proc. Amer. Math. Soc. 87 (1983), 375-377. MR 84e:54040
- [R2]
- J. T. Rogers, Jr., Completely regular mappings and homogeneous aposyndetic continua, Canad. J. Math. 33 (1981), 450-453. MR 83a:54012
- [R3]
- J. T. Rogers, Jr., Decompositions of continua over the hyperbolic plane, Trans. Amer. Math. Soc. 308 (1988), 277-291. MR 90a:54091
- [R4]
- J. T. Rogers, Jr., Homogeneous continua, Topology Proc. 8 (1983), 213-233.
- [R5]
- J. T. Rogers, Jr., Homogeneous hereditarily indecomposable continua are tree-like, Houston J. Math. 8 (1982), 421-428. MR 84b:54072
- [R6]
- J. T. Rogers, Jr., Orbits of higher-dimensional, hereditarily indecomposable continua, Proc. Amer. Math. Soc. 95 (1985), 483-486. MR 86k:54054
- [S]
- E. H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York, 1966.
- [W]
- J. J. Walsh, Dimension, cohomological dimension, and cell-like mappings. In ``Shape Theory and Geometric Topology'' (S. Mardesic, and J. Segal, eds.), Lecture Notes in Math, No. 870, Springer-Verlag, Berlin and New York, 1981, 105-118. MR 83a:57021
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
54F15,
54F50
Retrieve articles in all Journals with MSC
(2000):
54F15,
54F50
Additional Information:
James
T.
Rogers
Jr.
Affiliation:
Department of Mathematics, Tulane University, New Orleans, Louisiana 70118
Email:
jim@math.tulane.edu
DOI:
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
Posted:
February 14, 2003
Communicated by:
Ronald A. Fintushel
Copyright of article:
Copyright
2003,
American Mathematical Society
|
Comments: webmaster@ams.org