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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Cell-like 0-dimensional decompositions of $ S\sp{3}$ are $ 4$-manifold factors


Authors: R. J. Daverman and W. H. Row
Journal: Trans. Amer. Math. Soc. 254 (1979), 217-236
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 $ {S^3}$ into cell-like sets which is 0-dimensional, in the sense that the image of the nondegenerate elements in $ {S^3}/G$ is 0-dimensional, then $ G\, \times \,{S^1}$ is shrinkable, and $ \left( {{S^3}/G} \right)\, \times \,{S^1}$ is homeomorphic to $ {S^3}\, \times \,{S^1}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0539916-8
PII: S 0002-9947(1979)0539916-8
Keywords: 0-dimensional decomposition, cell-like decomposition, embedding dimension, thin cubes with handles, shrinkable decomposition, null sequence decomposition
Article copyright: © Copyright 1979 American Mathematical Society