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References
J. J. Andrews and M. L. Curtis, n-space modulo an arc, Ann. of Math., vol. 75 (1962), 1–7.
J. J. Andrews and Leonard Rubin, Some spaces whose product with E 1 is E 4, Bull. Amer. Math. Soc., vol. 71 (1965), 675–677.
R. H. Bing, A decomposition of E 3 into points and tame arcs such that the decomposition space is topologically different from E 3, Ann. of Math., vol. 65 (1957), 484–500.
_____, The cartesian product of a certain non-manifold and a line is E 4, Ann. of Math., vol. 70 (1959), 399–412.
M. Brown, A proof of the generalized Schoenflies theorem, Bull. Amer. Math. Soc., 66 (1960), 74–76.
J. R. Bryant, Euclidean space modulo a cell, Fundamenta Mathematicae, vol. 63 (1968), 43–51.
R. D. Edwards and R.T. Miller, Cell-like closed-O-dimensional decompositions of R 3 are R 4 factors, to appear in Trans. Amer. Math. Soc.
R. H. Fox and E. Artin, Some wild cells and spheres in three-dimensional space, Ann. of Math. 49 (1948), 979–990.
James Glimm, Two cartesian products which are euclidean spaces, Bull. Soc. Math., France, vol. 88 (1960), 131–135.
H. W. Lambert and R. B. Sher, Point-like O-dimensional decompositions of S 3, Pacific J. Math., 24 (1968), 511–518.
D. R. McMillan, Acyclicity in 3-manifolds, Bull. Amer. Math. Soc. 76 (1970) 942–964.
_____, Neighborhoods of surfaces in 3-manifolds, Mich. Math. J., vol. 14 (1967), 161–170.
_____, Local properties of the embeddings of a graph is a three-manifold, Canad. J. Math., vol. 18 (1966), 517–528.
D. R. McMillan, Jr., Cartesian products of contractible open manifolds, Bull. Amer. Math. Soc., 67 (1961), 510–514.
Leonard Rubin, The product of an unusual decomposition space with a line is E 4, Duke Math. J., vol. 33 (1966), 323–330.
_____, The product of any dogbone space with a line is E 4, Duke Math. J., vol. 37 (1970), 189–192.
_____, Recognizing certain factors of E 4, Proc. Amer. Math. Soc., vol. 26 (1970), 199–200.
_____, A general class of factors of E 4, Trans. Amer. Math. Soc., vol. 166 (1972), 215–224. (See also Erratum Trans. Amer. Math. Soc., vol.177 (1973), p. 505.)
J. H. C. Whitehead, A certain open manifold whose group is unity, Quart. J. of Math., (Oxford), 6 (1935), 268–279.
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© 1975 Springer-Verlag
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Pixley, C., Eaton, W. (1975). S1 cross a UV decomposition of S3 yields S1×S3 . In: Glaser, L.C., Rushing, T.B. (eds) Geometric Topology. Lecture Notes in Mathematics, vol 438. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066114
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DOI: https://doi.org/10.1007/BFb0066114
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