Cell-like 0-dimensional decompositions of 𝑆³ are 4-manifold factors

Daverman, R. J.; Row, W. H.

doi:10.1090/S0002-9947-1979-0539916-8

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