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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The ends of product manifolds


Author: Dennis C. Hass
Journal: Proc. Amer. Math. Soc. 36 (1972), 267-271
MSC: Primary 57A15
DOI: https://doi.org/10.1090/S0002-9939-1972-0307243-9
MathSciNet review: 0307243
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Abstract: In this paper we provide simple point set properties which characterize the m-spheres $ {S^m}$, open m-cells $ {E^m}$, closed cells $ {I^m}$, and annuli $ {A^m} = [0,1) \times {S^{m - 1}}$. It is important to notice that the Poincaré conjecture is not used in dimension 3 or 4.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0307243-9
Keywords: Topological manifold, generalized manifold, spheres, cells, annulus, product space, ends, Poincaré theorem, residual set
Article copyright: © Copyright 1972 American Mathematical Society