Abstract
We answer a question of J. Sternfeld by producing a topological 3-cell in four dimensional Euclidean space whose projection onto the plane of the first two co-ordinate axes is a 2-cell but whose projections onto the 3-spaces determined by the first, second and third as well as the first, second and fourth co-ordinate axes are also 2-cells. We generalize this construction in higher dimensions.
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References
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J. Sternfeld,Uniformly separating families of functions, Israel J. Math.29 (1978), 61–91.
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Pixley, C.P. A note on the dimensions of projections of cells inE n . Israel J. Math. 32, 117–123 (1979). https://doi.org/10.1007/BF02764908
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DOI: https://doi.org/10.1007/BF02764908