$(E^{3}/X)\times E^{1}\approx E^{4}$ ($X$, a cell-like set): an alternative proof
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- by J. W. Cannon PDF
- Trans. Amer. Math. Soc. 240 (1978), 277-285 Request permission
Abstract:
The author gives an alternative proof that a cell-like closed-0dimensional decomposition of ${E^3}$ is an ${E^4}$ factor. The argument is essentially 2-dimensional. The 3- and 4-dimensional topology employed is truly minimal.References
- J. W. Cannon, Taming cell-like embedding relations, Geometric topology (Proc. Conf., Park City, Utah, 1974) Lecture Notes in Math., Vol. 438, Springer, Berlin, 1975, pp.Β 66β118. MR 0391104
- Carl Pixley and William Eaton, $S^{1}$ cross a UV decomposition of $S^{3}$ yields $S^{1}\times S^{3}$, Geometric topology (Proc. Conf., Park City, Utah, 1974) Lecture Notes in Math., Vol. 438, Springer, Berlin, 1975, pp.Β 166β194. MR 0394672
- Robert D. Edwards and Richard T. Miller, Cell-like closed-$0$-dimensional decompositions of $R^{3}$ are $R^{4}$ factors, Trans. Amer. Math. Soc. 215 (1976), 191β203. MR 383411, DOI 10.1090/S0002-9947-1976-0383411-3
- D. R. McMillan Jr., Compact, acyclic subsets of three-manifolds, Michigan Math. J. 16 (1969), 129β136. MR 243501 J. H. C. Whitehead, A certain open manifold whose group is unity, Quart. J. Math. (2) 6 (1935), 268-279.
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 240 (1978), 277-285
- MSC: Primary 57A15
- DOI: https://doi.org/10.1090/S0002-9947-1978-0482770-2
- MathSciNet review: 0482770