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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Leonard R. Rubin
Journal: Proc. Amer. Math. Soc. 26 (1970), 199-200
MSC: Primary 54.78
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}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0266180-7
PII: S 0002-9939(1970)0266180-7
Keywords: Defining sequence, toroidal sequence, trivial sequence, cubes with handles
Article copyright: © Copyright 1970 American Mathematical Society