Cell-like closed-0-dimensional decompositions of 𝑅³ are 𝑅⁴ factors

Edwards, Robert D.; Miller, Richard T.

doi:10.1090/S0002-9947-1976-0383411-3

Cell-like closed-$0$-dimensional decompositions of $R^{3}$ are $R^{4}$ factors
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by Robert D. Edwards and Richard T. Miller

Trans. Amer. Math. Soc. 215 (1976), 191-203

DOI: https://doi.org/10.1090/S0002-9947-1976-0383411-3

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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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