Celllike 0dimensional decompositions of are manifold factors
Authors:
R. J. Daverman and W. H. Row
Journal:
Trans. Amer. Math. Soc. 254 (1979), 217236
MSC:
Primary 54B15; Secondary 57N99
MathSciNet review:
539916
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Abstract: The main result is the title theorem asserting that if G is any upper semicontinuous decomposition of into celllike sets which is 0dimensional, in the sense that the image of the nondegenerate elements in is 0dimensional, then is shrinkable, and is homeomorphic to .
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 J. W. Cannon, Shrinking celllike decompositions of manifolds. Codimension three, Ann. of Math. (to appear). MR 541330 (80j:57013)
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 W. T. Eaton and C. P. Pixley, cross a decomposition of yields , in Geometric Topology (L. C. Glaser and T. B. Rushing, editors), Lecture Notes in Math., vol. 438, SpringerVerlag, New York, 1975, pp. 166194. MR 0394672 (52:15473)
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 [E2]
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 W. H. Row, Jr., Compact sets definable by free 3mamfolds, Trans. Amer. Math. Soc. 197 (1974), 225244. MR 0362314 (50:14756)
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 , Approximation of compacta in in codimension greater than two, Mat. Sb. 90(132) (1973), 625636 = Math. USSRSb. 19 (1973), 615626. MR 0339194 (49:3957)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197905399168
PII:
S 00029947(1979)05399168
Keywords:
0dimensional decomposition,
celllike decomposition,
embedding dimension,
thin cubes with handles,
shrinkable decomposition,
null sequence decomposition
Article copyright:
© Copyright 1979
American Mathematical Society
