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It is proved that the product of a cell-like closed-0-dimensional upper semicontinuous decomposition of      R 3 {R^3}       with a line is      R 4 {R^4}      . This establishes at once this feature for all the various dogbone-inspired decompositions of      R 3 {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 {R^1}      .

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