Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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}$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 54B15, 57N99

Retrieve articles in all journals with MSC: 54B15, 57N99

Additional Information

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