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Recognizing certain factors of $ E\sp{4}$


Author: Leonard R. Rubin
Journal: Proc. Amer. Math. Soc. 26 (1970), 199-200
MSC: Primary 54.78
DOI: https://doi.org/10.1090/S0002-9939-1970-0266180-7
MathSciNet review: 0266180
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Abstract: It has been proved that for certain peculiar decomposition spaces $ Y$ of euclidean $ 3$-space $ {E^3}$ is homeomorphic to euclidean $ 4$-space, $ {E^4}$. In this paper we prove that if a decomposition space $ Y$ of $ {E^3}$ is generated by a trivial defining sequence whose elements are cubes with handles, and this sequence can be replaced by a toroidal defining sequence, then $ Y \times {E^1}$ is homeomorphic to $ {E^4}$.


References [Enhancements On Off] (What's this?)

  • [1] J. J. Andrews and Leonard Rubin, Some spaces whose product with $ {E^1}$ is $ {E^4}$, Bull. Amer. Math. Soc. 71 (1965), 675-677. MR 31 #726. MR 0176454 (31:726)
  • [2] R. H. Bing, The cartesian product of a certain nonmanifold and a line is $ {E^4}$, Ann. of Math. (2) 70 (1959), 399-412. MR 21 #5953. MR 0107228 (21:5953)
  • [3] Leonard Rubin, The product of an unusual decomposition space with a line is $ {E^4}$, Duke Math. J. 33 (1966), 323-329. MR 33 #3283. MR 0195078 (33:3283)
  • [4] Leonard R. Rubin, The product of any dogbone space with a line is $ {E^4}$, Duke Math. J. 37 (1970), 189-192. MR 0267548 (42:2450)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0266180-7
Keywords: Defining sequence, toroidal sequence, trivial sequence, cubes with handles
Article copyright: © Copyright 1970 American Mathematical Society

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