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


Authors: Robert D. Edwards and Richard T. Miller
Journal: Trans. Amer. Math. Soc. 215 (1976), 191-203
MSC: Primary 57A10
DOI: https://doi.org/10.1090/S0002-9947-1976-0383411-3
MathSciNet review: 0383411
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Abstract: It is proved that the product of a cell-like closed-0-dimensional upper semicontinuous decomposition of $ {R^3}$ with a line is $ {R^4}$. This establishes at once this feature for all the various dogbone-inspired decompositions of $ {R^3}$. The proof makes use of an observation of L. Rubin that the universal cover of a wedge of circles admits a 1-1 immersion into the wedge crossed with $ {R^1}$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1976-0383411-3
Keywords: Closed-0-dimensional decomposition, cell-like decomposition, cube-with-handles, window building
Article copyright: © Copyright 1976 American Mathematical Society

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