Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54.78

Retrieve articles in all journals with MSC: 54.78

Additional Information

PII: S 0002-9939(1970)0266180-7
Keywords: Defining sequence, toroidal sequence, trivial sequence, cubes with handles
Article copyright: © Copyright 1970 American Mathematical Society